2.x +1 1. For y = find an equation of the tangent line to the curve at (1, 1). Show your x+2 work to get credit. Find the derivative of the function using the definition of the derivative. State the domain of the function and the domain of its derivative. 2. f(x+h) – f(x) Definition of derivative: f'(x) = lim h→0 h а) f(x) = mx + b domain of f(x): domain of f'(x): b) 1 f(x) = domain of f(x): domain of f'(x): 3. Differentiate the function by using the differentiation rules of section 3.1. VI +x a) y = x2 b) k(r) = e" +re

Q: f(x+h)-f(a) a.) Find the derivative function, f'(x) = lim h-0 b.) Determine the slope of the curve,…

A:

Q: 27. y = x²(1 - In x²)

A: To find the derivative of the following function.

Q: 5. Compute derivatives of the following functions. You are not required to simplify your derivative…

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Q: 6. R(z) Vz3 8z4

A: ddxxn =nxn-1ddx1xn =-nxn+1 ddxx =-12x

Q: Find the derivative of y = tan 3x

A: Given function is: y = tan 3x We have to find the derivative of y with respect to x.

Q: Find the derivative of the function y= arctan x +x/1+x2

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Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: n. y= (x+Inx)

A:

Q: 1 EX-1- Find the derivative of the function : f(x)= /2x+3

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Q: Find the derivative using the definition 1- y = vx -1

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: