For each function, identify an inside and outside function. Write an expression for the derivative.
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For each function, identify an inside and outside function. Write an expression for the derivative. For...
8. [0/5 Points] DETAILS PREVIOUS ANSWERS Find the derivative of the function. f(t) = 43/2 log&(vt + 3) 1 3x?loge (Vx+3) 3 2 f'(t) = X + 2 2 ln(6)(x+3) x
LI Write the composite function in the form f(g(x)). [Identify the inner function v = g(x) and the outer function y = f(u).] = V1 + 8x (g(x), f(u)) = Find the derivative dy/dx. dx X
Q2) Find the derivative of each function a) f(1) = b) f(x) sin 1COSI 1+008 d) f(x) = (1 + x)'(1 - x)2 1 e) f(1) = 2009 1672 f). f() = ln(sec 0 + tan ) B): S(21) = 1n () h) y = (In(ax)? g(x) = ln(2.3 - 3x + 2) i) c) f(x) = sina
QUESTION 9 Apply the techniques of logarithmic differentiation to find the derivative of the given function f(x). [Hint: first take the logarithm of both sides and simplify using properties of logarithms. Then differentiate implicitly.) F) - ** (3x+1) {f(x) = {{x^2 (3x + 1)^3} /(sqrt(x^2 + 4))] } TTTT Paragi Arial 3 (12p *DOQ E T' T. . 15 25 Path: P QUESTION 10 Find the derivative of the following expression involving inverse trigonometric functions. g(x) = arctan x +...
Consider the function f(x) = x ln(3x+1) (a) Find the derivative (b) Write the linearization of f at x = 2 (c) Use your linearization to estimate f(2.5) (d) Draw a sketch of the function in the space below, using a solid line for f(x). On the same coordinate plane, draw a sketch of the linearization using a dotted line. Please use values 0<x<5(or equal to) on the x-axis (e) Is your estimate from part c an overestimate or underestimate?
4. g(t)= 3. y=sin(tan5x) In problems 1-5, find the derivative of the function. Write your answers in simplest form. 1. f(x)=- sinx 2. f(x)=(x +7x-2) 100 1-COS X 3. y =sin(tan5x) 4. g(t)= t+3 5. f(x) = cos(x'cscx) sin(x-3) 6. Find lim 2-3 3x-x?
3. (a) (3 points) Write the definition of the derivative of a differentiable function f() at r = a; (b) (7 points) using the definition of derivative as in (a), find the derivative of the function f(x) = at a = 2.
3. (8 points each) Find the derivative of each function. Show as much work as possible. Do not simplify your answer. 2 (a) f(x) = x-0.5(1 – e2) + 4* + x4 x 2 93 (b) P(t) = + 2-t2 5+5e-3t (c) k(x) = 3 ln(2x +1) VX-5
SHORT ANSWER. Write the word or phrase that best completes each Evaluate the expression using the values given in the table 1) (fog)(4) 5 10 12 f(x) -4 10 3 14 1 X -5 1 -4 4 g(x) 1-5 5 10 Evaluate the expression using the graphs of y f(x) and y = g(x). 2) Evaluate (fg)(1) 8 g(x) one function to e For the given functions f and g, find the requested composite fu 1 2 3) f(x)= g(x)=-;...
Write a function that finds the derivative of a function f at a value x. It takes a function pointer f as argument that represents the function for computing the derivative. The derivative of a function can be calculated by f(x stepSize) - f(x- stepSize) 2*stepSize Use 0.01 for stepSize.