The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by f'(t) = 2130 + (12)ť², where t is measured in years since 1991. If the company is worth $35000 in 1991, what is it worth in 2000? Value in 2000:

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x?

A:

Q: B) Using the definition of derivative, find -if y = dx 1-x

A:

Q: Find the derivative. y = e(lnx)2

A: dydx=ddx e(lnx)2        =e(lnx)2 ddx2(ln x)         =e(lnx)2 2x

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

A: Here given Use the formula of product rule of derivatives as

Q: find the derivative using logarithm of y= (x+2)^2

A: Take ln on both sides Then differentiate both sides with respect to x

Q: Find the nth-order derivative of the function y=x3sin2x.

A:

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: Find the derivative gx) = 4 K) = cost dt

A: Problem is solved using Leibniz rule

Q: Find the derivative of the function. y = x2 ln x

A: We use the product rule to find the derivative

Q: Find the thousandth derivative of  f(x)  = x e-x

A:

Q: Find the derivative of function. y = log(2x)

A: A composite function is differentiated as follows: ddxfgx=f'gx·g'x

Q: Find the derivative of f(y)   f1(y) = ?

A: The given is: fy=6tany-y6-8y4y This function can be written as:…

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: Which function has the same derivative function f (x) as g(x) = lnx + x² – x?

A: we have to find derivative

Q: tind the first derivative of the fanction i2 () =メ ニフ(x-1)

A:

Q: y = kx xe

A: y=xe-kxTo solve the derivative

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

Q: A) Find an equation of the line tangent to the function of x + (y-x)' D9 atx 1. B) Using the…

A: Part A,Given,          The function is x2+y-x2=9 at x=1.

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: find the derivative. y = ln(t5t )

A:

Q: Find the derivative. y = e(ln x)2

A:

Q: What is the derivative of y = e2 +1, with respect to x?

A: Formula used

Q: how do you find the second derivative of f(x)=ln(x)?

A: on differentiation we get

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: Use the chain rule to find the derivative of 2e9z7 Use e^x for e".

A:

Q: what is the derivative of this question with solution y= csc (4x² ) Arccsc (4x² )

A:

Q: sinh(3x) g(x) 3

A:

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

A:

Q: (d) y = xnz²

A:

Q: Excrcise 10. Find the derivative d -7x * [" (t³ + 2) dt dx

A: Given,          ddxx∫57xt3+2dt

Q: Find the derivative of the function. Vs - 1 f(s) = Vs +5 l'(s)=]

A: Given query is to find the derivative of the function.

Q: The derivative f'(a) represents the instantaneous rate of change of y = f (x) with respect to x when…

A: Given that we need to check  behaviour of  the statement " The derivative f'(a) represents the…

Q: dy Find dx if y = v5 – x2 ,by using definition .)باستخدام صيغة تعریف المشتقة) formula of derivative

A: Given y=5-x2We know that f'(x)=limh→0f(x+h)-f(x)h...(1)f(x+h)=5-x2-2hx-h2f(x)=5-x2Put all these…

Q: Find the second derivative of the function. f(x) = sec x * "(x) = Noc

A: Please see the explanation below

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: (b). Find the second derivative. y=x²-5vx

A:

Q: dx 2 x--1

A:

Q: dy Find dx if y = V5- x2 , by using definition .)باستخدام صيغة تعريف المشتقة( formula of derivative

A:

Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

A: instantaneous rate of change of a function is differentiation of function at that point

Q: Which is the first derivative of y=vx ?

A:

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

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

A:

Q: Find the derivative of the power function y=xn.

A: y= xn To find the derivative of y

Q: y = (3x + 4)², solve for y' using derivative of nth power.

A:

Q: Find the 1st derivative of the function: y = 4(Vx + 1)5

A: Given that: y=4(x+1)5

Q: Which is the first derivative of y=vx ? *

A: Given Data: y=x Formula: d(xn)dx=nxn-1