Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos (2x² + 3)] f(x) =Gn Ve** +1)

Q: y = In (x* + 5)³

A:

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Find the Derivative f(x) = cosh(In(4x))

A:

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Find the derivative of f(x) = tan tan (3x2+2x)( Ans: (6x + 2) sec2 (3x2+2x) solution?

A: Let,

Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x 12x+6 бх2+бх-4 1 (6x2 + 6x – 4)aretan x…

A:

Q: Find the derivative of f(x) = In [sin(x) +x] Lsin(x)-x] %3D 2(sin x – x cos x) x2 - sin? x )2(x cosx…

A:

Q: Find the derivative of f(x)=sin sin(5x

A:

Q: Use logarithmic differentiation to find the derivative of the function. y = (cos(4x))* y'(x) =…

A: In this question we have to find differentiation by using logarithm.

Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

A:

Q: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: What is the derivative of 2(x)ln(x)+x

A:

Q: Note that 7 cos(x) In(x) is a product. Therefore, its derivative is given by (7 cos(x)) (In(x))

A:

Q: Find the first derivative of: y=〖sec〗^4 x-〖tan〗^4 x y=xArcsinx + √(1-x^2 )

A: We have to find the derivative of the given function.

Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: The derivative of sec2 2x(cos2x−sin2x) with respect to x is

A: Given: f(x)=sec2 2x(cos2x−sin2x)   Simplify the function before finding the derivative: By  the…

Q: show that nth derivative of  f(x)=x^2/(2x+1)(2x+3)

A: nth derivative of f(x)=x2(2x+1)(2x+3) f(x) can be written as by using synthetic division method…

Q: What is the derivative of x 3 sin(x)? Select one: (sin(x) + 3x cos(x)) 2 Зх 3 + cos(x) 2 Зх 3 2 O…

A: Derivative of the function

Q: The first derivative of y=cos(tan(x2-7x+1)) is.. 1. O -[sin(tan(x²-7x+1))][sec²(2x-7)] 2. O…

A: Find the derivative of y=costanx2-7x+1

Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

A:

Q: Find the 46th derivative of y = cos (x) sin (a) cos (2) cos (x) - - sin (x)

A: Given y=cosx

Q: What is the anti derivative of  f(x)= 2sin(x)-sec2(x)

A: Given information

Q: 11 In(x)sin (x²). Find the first derivative of g(x) (x),6

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: Determine the derivative of y = ln(4x² - 2x). O 8x-2 4x-1 8x-2 4x²-x 4x-1 4x²-x 4x-1 2x2- -x O O

A:

Q: Find the derivative ofƒ(x) = 1/x5in two different ways:using the Power Rule and using theQuotient…

A: given: f(x)=1x5 the differentiation of the function f(x)=1x5 by using the power rule is: the…

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

A:

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

A:

Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

A:

Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

A:

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

A:

Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

A:

Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: what is the first derivative of cosx^2(x^2+2)

A:

Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

A:

Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: What is the derivative of 2x cos x ? 2 cos x - 2x sin x 2 cos x+ 2x sin x -2 sin x 2 sin x 2x-sin x

A:

Q: 10. Find the first derivative: f(x) = (x³ + 2x) In x %3D

A:

Q: k(x) = x In x %3D

A:

Q: In(cos(x)) Find the derivative of cos(In(x))

A: Derivative using quotient rule (f/g)'=(gf'-fg')/g2

Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 5. Find the derivative of --( 1 + sin 0 cos 0

A:

Q: 2 12. f (x) = (1tsinx) Cosx

A:

Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

A: Given  f(x) = sinxx we have to obtained the first derivative of f(x) by using  Richardson's…

Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

Q: 5-cos x 3) f(x) = 5+sinx foo

A:

Q: 1.Find the derivative of y = - arcsin %3D V4-x2

A: Given:        y=x4-x2-arcsinx2 differentiating on both sides     dydx=ddxx4-x2-arcsinx2…