a. Use the definition of the derivative and the identity sin(a + B) = sin(a) cos(B) + cos(a) sin(B) to prove that [sin(x)]' = cos(x). %3D

Q: The derivative of any constant is 0. The well-remembered triq identity tells us that sin2(x) +…

A: To verify that sin2(x) + cos2(x) is a constant, we need to show that the derivative of sin2(x) +…

Q: (5x) S sin(x) tan(x) .........

A:

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: 1) Find the derivative of y = e" tan x

A: As we know that; The chain rule; fgx'=f'gx·g'x And ddxex=exddxtanx=sec2x Given: y=etanx

Q: II. Give the indicated derivative 1) find the 27th derivative of cos x

A:

Q: 2. Find the derivative of the following functions: (a) g (0) = 77² (sec 0 - sin 20)²

A:

Q: Find the derivative of the 6. sin 80 (f) f(0) = %3D 1+ cos 80

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: sin(z)+9 cos(z)–9" Find the derivative of If you need to enter an expression like sin x with STACK,…

A: To find  The derivative of given expression.

Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

A:

Q: What is the derivative of 0.50 sin 2t+0.30 cos t

A:

Q: f (x) = sin (cos(tan x))) find its derivative

A: Consider the provided function, fx=sincostanx Find the derivative of the function with respect to x.…

Q: Select the derivative of the following function from the potential answers Select one: O a. O b. O…

A:

Q: Find the derivatives of the functions

A:

Q: Find the derivative of y = cos 12 with respect to x. |

A: Given : y = cos-112x

Q: Let f(x) 3 sin(cos x) = f'(x) =

A: Using chain rule of differentiation.

Q: What are the derivatives of sin g(t), cos g(t), and tan g(t)?

A: we have to find the derivatives of sin g(t), cos g(t), and tan g(t)

Q: Find the derivative of the given function:

A:

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: