show that the function is derivable and that the derivative is continuous.

Q: Use the definition of the derivative to find the slope of the tangent line to the graph of the…

A:

Q: Find the derivative of the transcendental function. 6e* y' =

A:

Q: Find the derivative of the function.

A: Given: To find: Derivative

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

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: Define the derivative of f(x) at x

A: Consider a function f(x) The differentiability of a function:  Let f(x) be a real valued function…

Q: Define the derivative of f(x) at x =a

A: For a function f(x), the derivative is defined as: Now at x=a, the derivative is defined as:

Q: f(x)= xe* In(x³)

A: f(x)=xe-xln(x3)According to question we have to calculate the derivative of the function.

Q: find the derivative of the transcendental function y=e^x-cotx

A: Given,             y=ex-cotx

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

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

A:

Q: Find the derivative of the function f(x) = arccot √x

A:

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: f(x)= 2

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

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

A: The function is given as F(x)=∫xx2et4 dt. The Leibnitz rule of differentiation under the integral…

Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: Find the derivative of the function. f(x) = 2x In(x) f'(x) =

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

Q: Calculate the derivative.

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 that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

A:

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

A:

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: f(x) = x In x

A:

Q: Is the function f(x) = |x| cos x differentiable at the point x = 0 ? (Use definition of the…

A: if lim∆x→0f(∆x+x)-f(x)∆x doesn't exist then not differential

Q: Let f(x) = x8 - 8x6. When the tangent line is vertical, what is the derivative of f(x)?

A: Here we will understand the vertical tangent line and we will find derivative of given function,

Q: Give a nonzero function that is its own derivative

A: Consider the function fx=ex.

Q: Is the functionf(x) = |x| cosx differentiable at the point x =0 ? (Use definition of the derivative)…

A:

Q: Give a justified example of function f(x) that is differentiable everywhere, yet its derivative has…

A: Definition of Differentiability p(x) is said to be differentiable at the point x = b if the…

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

A:

Q: Find the derivative of the function f(x) v4-x by definition

A:

Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: What is the first-order derivative of y = x^y?

A:

Q: On which open interval is the derivative positive/ negative .

A: Given:

Q: e of the derivati

A: It is given that ,  x j(x) j'(x) k(x) k'(x) -1 3 -4 5 -6 a) h(x)=2j(x)k(x)find h'(-1)=? b)…

Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: Calculate the derivative using the appropriate rule or combination of rules. et f(x) = (e + 2)(x +…

A:

Q: Use the Fundamental Theorem of Calculus to find the derivative. dt

A: We have to find the derivative by fundamental theorem of calculus.

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

A:

Q: Calculate the derivative of the function y=x2−x−1x without using the quotient rule.

A:

Q: find the derivative that function  f(x)=xsinx

A: Given,          fx=xsinx

Q: Compute for the derivative of 3 y = х |

A:

Q: Use the definition of derivative to find the tangent and normal equations of f (x) = (x – 3)2 %3D

A:

Q: Show that e is entire function.Find its derivative

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: