d [g(sec(2y))] dy

Q: Find the derivatives of the following functions. g(x) = x² cos(x).

A: The solution is given below in the next step:

Q: Find the derivative of the function g(x) = 3arccos(x/2)

A:

Q: Evaluate the derivatives of the following functions.

A:

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists.   h(x) =…

A:

Q: Evaluate the derivatives of the following functions

A:

Q: Find derivative of the following function. 5x -5x y%3D dy

A:

Q: Determine the derivative of the following functions. Show your complete solutions and simplify the…

A:

Q: Evaluate the derivatives of the following functions.

A: ddxarcsin(esin(x)=11-(esinx)2·ddxesinx=esinx·ddxsinx1-e2sin(x)=esinxcos(x)1-e2sin(x)

Q: Obtain the derivatives of the following functions f(x) and enter your answers as functions of æ in…

A:

Q: F(y) = In(1 – 5y² +y³)

A: Topic = Derivative

Q: Find derivatives of the functions defined as follows: y = 73x+1

A: y=73x+1ory=73x·7ory=7·73x Use formula of derivative ddxax=axln a

Q: Find the derivative of the following function F(x)=(from x^3 to x^4)∫(2t−1)^3dt

A:

Q: Obtain the derivatives of the following functions f(x) and g(æ) and enter your answers as functions…

A: Given functions are, f(x)=54(28x+9)9, g(x)=75ln25x+7 Differentiating f(x) with respect to x we get,…

Q: Evaluate the derivative of the following functions at the given point  ƒ(t) = t2; a = 2

A:

Q: Evaluate the derivatives of the following functions.

A: fy=tan-12y2-4

Q: Find derivatives of the functions defined as follows:

A: Given: fx=ex3x+2

Q: Use the rules for derivatives to find the derivative of function defined as follows. g(z) = log2(z3…

A: The first derivative of ln(x)=1x. The function loga(x) can be written as ln xln a hence its first…

Q: Find derivatives of the function defined as follows. y = e-8x

A: We have to find derivatives of the function: y=e-8x We know the formula of derivatives,…

Q: xtany + y'secx = = e3y e3y

A: The given equation is x. tany + y2. secx = e3y The function is given by f(x, y) = x. tany + y2. secx…

Q: Find the derivative of the following functions. Write your answer on a separate sheet of paper. 2.…

A:

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. g(x) = 2x2…

A: Given function is gx=2x2-3x. We know that, f'x=limx→cfx-fcx-c Using the above formula of derivative,…

Q: Find derivatives of the function defined as follows.

A: Consider the given function as y=ex+e-xx

Q: Find derivatives of the functions defined as follows: y = (x + 3)2e4x

A: Chain Rule of differentiation: ddxf(g(x))=f'(g(x))g'(x) Product Rule of differentiation:…

Q: Evaluate the derivatives of the following functions.

A: Given function is fx=cos-11x. To find the derivatives of the function. Solution: Chain rule of…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = x3…

A: Given: fx=x3+2x2+1 , c=-2 To determine: Derivative of given function at x=c

Q: Q1:- Find the first order derivative of each of the following functions: c) y sin x = x tan y

A:

Q: Use the rules for derivatives to find the derivative of function defined as follows. h(z) = log(1 +…

A:

Q: Use the h → 0 definition of the derivative to find f'(0) for f(x) I+1

A:

Q: In the given question , use the alternative form of the derivative to find the derivative at x = c,…

A: g(x) = x2- x, c = 1

Q: f(t) g(t) d (a) dt

A:

Q: (c) y = e* sin 7x + In(cos(x)) (d) y= xarcsin x+ V1-x²

A:

Q: Find the derivatives of the function defined as follows.

A:

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. (If an…

A:

Q: Find derivatives of the functions defined as follows:

A: Given that : The function is y = tet + 2e2t +1 .

Q: Find the derivatives of the functions k(x) = x2 sec (1/x)

A:

Q: Find the second order derivatives of the following functions f(x) 3x - x' i) Tan 1-3x

A:

Q: Find the derivatives of the following functions using derivative shortcuts a) f(x) = sec( sqr(x…

A:

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists. f(x) = (x…

A: Given function is fx=x-623. To find the derivaitve of the function at x=c. Differentiating with…

Q: Find the derivatives of the functions defined as follows. y=12tan(9x+1)

A: Given: y=12tan9x+1

Q: Evaluate the derivative of the following function at the given point. x+ 3x - 5y + 101 = 0: (-3.4)…

A: The objective is to evaluate the derivative of the function at the given point.

Q: Evaluate the derivative of the following function: f(x) = cos^-1 (1/x)

A: Given function

Q: Find the derivatives of the following functions with respect to x  x=tan (e-y)

A:

Q: Compute the derivative of the following function. f(x) = 2 e 2x f'(x) =L %3D

A: To find the derivative

Q: Find derivatives of the functions defined as follows: . y = 1.2e5x

A: the given function is: y=1.2e5x we have to find the derivative of the given function.

Q: Q1: Find the 4th derivative of the following function. F(x) = sin x cos x %3D

A: To find the derivative of the given function

Q: The derivative of the following function at x = 1 y = tan-1V4x3 – 2 is 2 O 0.5 1.4142 O 0.707

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (2x2 -r+1) In(x)+2(cos(z² +3)| f(x) =

A: Quotient rule of differentiation:…

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: