Give two different interpretations of the derivative of the function y = f(x) at x = a.

Q: Find the derivative of the function. f(x) = 4e* – x2 f'(x) =

A: Simply use the power law of derivative and also derivative of exponential .

Q: Find the second derivative of the following function: f(x) = esinx %3D

A:

Q: Find the second derivative of the function. f(x) = x cos(x) f"(x) =

A:

Q: What is the derivative of the function f(x) = e-2x?

A:

Q: Find the derivative of the function. r(x) r'(x) =

A: Consider the provided function, rx=e4x29 Find the derivative of the provided function.

Q: Find the derivative of the function. y'(x) =

A:

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

A:

Q: Find the derivative of the algebraic function.

A:

Q: please show ALL your steps

A: we are given a function

Q: What is the millionth derivative of f(x) = e x ?

A: ex

Q: Find the derivative of y = (x - 1) 2× + 1 at x = 2.

A:

Q: Find the derivative of the function g(x)= tanx/e^x.

A: This problem can be solved by the quotient rule in derivatives.

Q: Find the derivative of f (y) = 153/g In(y)

A: Given: f(y)=15y3lny

Q: What is the derivative of f(x) = - 3 with respect to r? %3D

A: Given: The function f(x)=-3x3

Q: What is the derivative of y=e^x?

A: The derivative of a function y=f(x) gives the rate of change of that function with respect to x.…

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: What is the second derivative of f (x) = e²?

A:

Q: Find the general anti-derivative of f(x) = + Vx on a continuous interval.

A:

Q: Find the derivative of the function.

A: Given: f(x)=log2x2x-1

Q: Evaluate the derivative at x = 1 for y = I (

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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

A: Given:            fx=esinx   differentiating on both sides with respect to x.           f'x=ddxesinx…

Q: Find the derivative of the function. 3x2 g(x) • dt 4 + t3 tan x g'(x) =

A:

Q: Find the derivative of the function: f(x)= e^x÷x^2

A: Given,

Q: Find the derivative of the function. f (x) = 1/ ( 1+ sec x ) 2

A: Consider the given function, fx=11+secx2 it can be also written as, fx=1+secx-2 now differentiate…

Q: Find the derivative of the function Зх + у Зx + y = Зх

A: Given function,

Q: Find the derivative of the function. 5. x + 2 y = e y' =

A: The given function,     y=ex7+25

Q: Use the alternative form of the derivative to find the derivative at x = c (if It exists). f(x) = x2…

A: Given f(x)=x2-2 c=5

Q: Compute for the derivative of the function below for x = 1. f(x) = 2xe

A: Solution: dydxx=1=2xex

Q: Let y=x(lnx)^2. Find the value of x for which the second derivative y"(x), equals zero.

A:

Q: Find the derivative of the function. F(x) = dt

A:

Q: Find the derivative of the function y=(x−1)(x−2)(x−3) at x=0.

A:

Q: Find the derivative of the function. f(x) = logg(x) f'(x) =

A: Derivative Question

Q: Find the second derivative of the following function: f(x) = esin1, %3D

A:

Q: Find the derivative of the function. f(x) = ex - xe

A:

Q: Find the derivative of the function y=√x(1+x).

A: The given function is y=x1+x. We know that, by chain rule of differentiation fg'=fg'+gf'

Q: Find the given flx), + 2x derivative of function. %3D a+x

A:

Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

Q: Find the derivative of the function. r(x) = r'(x) :

A:

Q: Find the derivative of the function. F(x) = dt F'(x) =

A:

Q: Find the derivative of the function. y = x*V25 - x²

A:

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function f(x)=(x²+e* + sin x)*.

A:

Q: What is the second derivative of * f(x) = e²?

A: We have to find second derivative of the function: fx=ex2 We know the formula of derivatives,…

Q: Find the derivative of the function. g(x) = log,(x) g'(x) =

A:

Q: Evaluate the first derivative of the function below at (1, -2). y X - - + + + 1/4 = 5 y x

A: Given: xy+yx=5   As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Power Law: ddxxn=nxn-1

Q: Find the derivative of the function. f(x) = /2 + V1+ Va f (x) = ||

A:

Q: Find the derivative of the function y=√x.

A: Given, y=x

Q: Find the derivative of the function: f(x) = Vx + Vx + 1 1 +

A:

Q: Find the derivative of the function. h(x) = ex + 5

A: First we will differentiate exponential part then we eill differentiate algebraic part

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: