27. f(t) = ;a = 9,

Q: Use the rules for derivatives to find the derivative of function defined as follows.

A: The derivative gives the rate of change of a function. It gives the slope of the function at a point…

Q: Obtain the derivative of any of the following functions: A) f(x) = 3cotg²3x B) f(x) = 6cos7(3x2 - 1)

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

Q: f(x+h) – f(x), Use the definition of the derivative (that is, f'(x) = lim h0 3 = 3r2. dr to show…

A:

Q: Use the limit definition of the derivative to find f(x) for the given functions and given value: 3…

A: Given data: *The function f(x) is f(x)=3/(x-2). *The point at which the derivative required is at…

Q: For the function ƒ(x) = 2* we use the two-point formula to approximate the first derivative of f at…

A:

Q: use the chain rule to find the derivative of the following function: f(x)=10cos^3(4x)

A:

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

A:

Q: f(x +h) – f(x) lim h f(x) = 3x2 – 10x + 6 1.

A: Given  The function are  1) fx=3x2-10x+6 5) fx=8x    Formula :- f'(x)=limh→0fx+h-fxh .

Q: Use the rules for derivatives to find the derivative of function defined as follows. q = (e2p + 1 -…

A: Use the rules for derivatives to find the derivative of function defined as follows. q = (e2p + 1 -…

Q: Consider the second derivative graph, y = f"(x), %3D given below. Which of the following statements…

A: Graph f''(x) is given, we have to find the concavity if the graph f(x).

Q: If f' is the derivative of f with | f'(x) dx = 10 and f(2) = 4, then f(1) :

A:

Q: Use the limit definition of the derivative to find the function f' for the following function.…

A: Limit Definition of the Derivative: We define the derivative of a function f(x) at x=a as.  f'(a)…

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

A:

Q: Find derivatives of the functions defined as follows:

A: Given: fx=ex3x+2

Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

A: ddxxn=n xn-1

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 the derivative f(x) of the following function with respect to x m 2 fm(x) = Σ n n=1

A:

Q: The derivative of the function f(x) = elan(=) + Ve is

A:

Q: Given the function f(z) shown, which is the graph of the derivative f'(z) ?

A:

Q: Given

A:

Q: b) f(x) = xe

A: If f(x) is a function of x and the second derivative of f(x) exist at any stationary point x0.1.If…

Q: Use the formula f(x + h) – f(x) f'(x) = lim %3D h→0 h to find the derivative of the following…

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: Use the following derivative function ?′f′ to determine the local minima and maxima of the function…

A: Consider the equation

Q: Find the derivative f'm(x) of the following function with respect to x:

A: Consider the given function:

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

A: To find derivative: f(x)=x-6,c=6. Solution: By definition:…

Q: A. f(x) = 2x4 + 5x² %3D slop

A:

Q: Compute the derivative pf the given function and find the equation of the line that is tangent to…

A:

Q: Given the graph of a function y = f(x) below, select the representation that best corresponds to the…

A: Graph of the function given,we have to find derivative of the function.

Q: Let f(x) = x – 5x. Calculate the difference quotient f(2+h)-f(2) for h = -.1 If someone now told you…

A: Given that

Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: Compute the derivative of the following function. f(x) = 3x e 3x f'(x) = O

A:

Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Use the following derivative function f' to determine the local minima and maxima of the function f:…

A: Consider the provided question,

Q: Find the derivative of the function by the limit process. g(t) = t³ + 6t g'(t) =

A: We can find the answer as below.

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: If f(x) is a differentiable function such that f(3) = f'(3)%=D4, compute the following derivative.…

A:

Q: Find the derivative of the following function using the formula. f(x + h) – f(x) lim h-0 h f(x) =…

A: I am attaching image so that you understand each and every step.

Q: 1. For the following functions y=f (x), find f ' (a) by using the definition of derivative at a…

A: Here we use the definition of derivative.

Q: Let f(x)= e^x^2 . Find an equation of the line tangent to the graph of f at the point the (1,e).

A: Tangent to the graph,

Q: a. Compute the derivatives of the following function: sec(xy) = 4x(3x+ 5)5 b. Find an equation for…

A: Product Rule of differentiation : d(u.v)dx=u.dvdx +dudx.v dxndx = nxn-1 Equation of line passing…

Q: Find the value of the derivative (if it exists) at each indicated extremum.         g(x) = x + 4/x2

A:

Q: Find the derivative f(x) of the following function with respect to x: fm(x) = > n=D1

A:

Q: Consider the function (x) = -2r (a) Using the limit definition of the derivative, find f'(1). (b)…

A: (a). As we know that the expression for the derivative, according to the definition of limit is:…

Q: Let f(x) = 3x² + 2x − 10; a = 1. 1. Use the definition to find the derivative function f' 2. Find an…

A: The given function is: f(x)=3x2+2x-10

Q: Use the limit definition to compute the derivative of the function at  t = 3.   f(t)= t-3t2   f…

A:

Q: Find the derivative f (x) of the following function with respect to x: 2 fm(x) = Σ n* · x" n=1

A: We havefm (x) = (∑n=1m nx xn)2 We expand this series : fm (x) = [1x+2x x2 +3x x3+4x x4+......+mx…

Q: Consider the function defined by f (x) = -x + ae" where a E R: (1) find a such that the graph of the…

A: To Determine: Consider the function defined by f(x)=-x+aex-1 where a∈ℝ find a such that the graph of…

Q: Find the derivative of the function by the limit process. h(s) = −2√s

A: h(s) = −2√s

Q: Consider the following function: f(x) = 3x – 2x? a. Find the derivative function f'(x) using the…

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: