Could you please find the derivative of the followong using the power rule: f(x)= 8/√x f'(x)=?

Q: Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Given f(x)=(1+2x2)(x-x2) By Product rule,…

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function. f (x) = cube root of ( 1+ tant )

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Q: Find the derivative. Simplify where possible. hx) = (1 - cosh x) /( 1 + cosh x)

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Q: use the definition of derivative to find the equation of the tangent line to the graph of f(x) = x2…

A: To find the equation of tangent line at the given point.

Q: Find the derivative using the appropriate rule or combination of rules. y = tan(x2 + 4x)

A: Consider the given function y = tan(x2 + 4x)

Q: Calculate the derivative of the function below using the quotient rule. y = Vx + 4x7

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Q: f(x) = Arctan csc² ( 3x

A: Some derivative formulae: ddxtan-1x=11+x2ddxcscx=-cscx cotx Chain rule of derivative:…

Q: Find the derivative. Simplify where possible.  f(x)= ex cosh x

A: Given function is

Q: Find derivative of function. y= sin square root of 1+x^2

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Q: 2 - x f(x) = 3 x + 1

A: given that f(x)=2-x3x+1we need to find the derivative of the functionuse the quotient rule that is…

Q: y = tan(x² + 4x)

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Q: Find the derivative using the long method y = sec x

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Q: Find the derivative of ƒ (x) = /9 – 2æ. To enter va, type sqrt(a). f' (x) =

A: The chain rule says that when the terms inside a function being differentiated does not correspond…

Q: find the derivative oof 1/x^3 + 3* 1/square root of x

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Q: Find the derivative using the Four-step rule f(x)=x/1-x

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Q: F(x) 1+ xe

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Q: Find the derivative of the function without using the Quotient Rule. y =

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Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Find the derivative. Simplify where possible. f(x)  =x Sinhx   - Coshx

A: Given f(x)  =x Sinhx   - Coshx

Q: f(x) = Vet + evi

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Q: Find the derivative of the function (slope of the tangent) using the definition at the point Xo=9…

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Q: Find the derivative of  y=ln [tan-1(7x5)] with respect to x.

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Q: Use the Product Rule or the Quotient Rule to find the derivative of the function y = sin x/x4

A: ddxxn=n xn-1 Quotient rule f(x)g(x)'=f'(x)g(x)-g'(x)f(x)g(x)2

Q: tanx – 9(x) 6 – secx

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Q: Find an equation of the tangent line to the graph of f ( x ) = 2x2 - 10 over 2x - 2 at the point on…

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Q: Find the derivative of the function two ways: by simplifying the function first and by using the…

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Q: Find the derivative at the given x-value with the appropriate rule. y=4-18sqrt x at x=4

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Q: If f(x) = x³ + find f"(-1).

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the derivative of ry = -3+x*y° using implicit differentiation.

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Q: By using the definition of the derivative, find the equation of the tangent line to the graph of…

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Q: Calculate the derivative of the function below using the quotient rule. 28 y = Va + 8x7

A: We have given a function and we have to find its derivative using quotient rule.

Q: Find the derivative of the function by using thẻ Product Rule. Simplify your answer. f(x) = (Vx -…

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Q: Find the derivative. Simplify where possible. y = x tanh-lx + In /1 – x²

A: We have to find

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: What is the derivative of f(x) sec(tanx)?

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Q: Find the derivative and simplify: f(x)=ex-cotx

A: To determine the derivative.

Q: Find the derivative of y with respect to x for y=2x   ???

A: y=2x

Q: What is the expression/value for true error in calculating the derivative of sin (2x) at x = 1/2 by…

A: See answer below.

Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: Calculate the derivative of y=tanx using the quotient rule.

A: Given that, y=tanxy=sinxcosx        Using tanx=sinxcosx

Q: How would you find the 65th derivative of sin(x)? Is there a pattern that occurs that allows you to…

A: Let y = sinx.Compute the first derivative of y as follows.

Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: By using the definition of the derivative, find the slope of the tangent line to the curve y = 4x −…

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Q: h (x)= 3

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Q: Find the derivative of f(x) = 3/x at x = 3 by using the definition of derivative. Note that you will…

A: Given,f(x) = 3x at x = 3

Q: function

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Q: Find the derivative of the function f(x) = 6x2 - 6 cosx

A: the given function f(x)=6x2-6 cos x

Q: f(x) = 7xe

A: We can find the answer as below.

Q: Find the derivative of the given function by using definition of derivative  f(x)= sec(x)

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