Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Chapter G, Problem 49E
To determine
To prove: If
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Find the derivative of:
a. 1/x^3 + 3 1/ square root of x
b. x^3+2x over x^2+3x+ pi^2
c. (2x^3+3x+1) ^1/3
d. e^3x^4 + 2x
e. ln(3x^2+e^x)
Shows the derivative function of:
u³ + 2u, where u = x² + 3
Evaluate the 3rd derivative of M with respect to (x)
M= x6 y3 Cos (x6 y3) if x =6 and y= 3
Chapter G Solutions
Single Variable Calculus
Ch. G - Evaluate the expression and write your answer in...Ch. G - Prob. 2ECh. G - Evaluate the expression and write your answer in...Ch. G - Prob. 4ECh. G - Prob. 5ECh. G - Prob. 6ECh. G - Prob. 7ECh. G - Prob. 8ECh. G - Prob. 9ECh. G - Prob. 10E
Ch. G - Prob. 11ECh. G - Prob. 12ECh. G - Prob. 13ECh. G - Prob. 14ECh. G - Prob. 15ECh. G - Prob. 16ECh. G - Prob. 17ECh. G - Prob. 18ECh. G - Prob. 19ECh. G - Prob. 20ECh. G - Prob. 21ECh. G - Prob. 22ECh. G - Prob. 23ECh. G - Prob. 24ECh. G - Prob. 25ECh. G - Prob. 26ECh. G - Prob. 27ECh. G - Write the number in polar form with argument...Ch. G - Prob. 29ECh. G - Prob. 30ECh. G - Prob. 31ECh. G - Prob. 32ECh. G - Prob. 33ECh. G - Prob. 34ECh. G - Prob. 35ECh. G - Prob. 36ECh. G - Find the indicated roots. Sketch the roots in the...Ch. G - Prob. 38ECh. G - Prob. 39ECh. G - Prob. 40ECh. G - Prob. 41ECh. G - Prob. 42ECh. G - Write the number in the form a + bi. 43. ei/3Ch. G - Prob. 44ECh. G - Prob. 45ECh. G - Prob. 46ECh. G - Prob. 47ECh. G - Use Eulers formula to prove the following formulas...Ch. G - Prob. 49ECh. G - Prob. 50E
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- Find the differential of the function. u = 2x5 + 5arrow_forwardFind y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x and y = (e-x)/ 4x3+5arrow_forwardFIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM ( 1. y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y =e^3x−e^−3x/e^3x+e^−3x 5. x =t/t−1, y =t2/t2−1arrow_forward
- Find the first and second derivatives of the functions u =(x2 + x)(x2 - x + 1)/x4arrow_forward4- Calculate the second derivative of the function y = f (x) defined by the equationx3 + y3 +3xy + 3y2 + 6x + 6y =0 at the point x = 1arrow_forwardThe derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)arrow_forward
- Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x). In all cases, a, b, c are real constants, and y is a function of x.arrow_forwardFind the differential of y=x^4-2x^2arrow_forwardFind the first derivative of y with respect to x (y') of the given function. 1. x^2 y - xy^2 + x^2 + y^2 = 0arrow_forward
- • Show that both of the functions f(x) = (x − 1)^4and g(x) = x^3 −3x^2 + 3x+ 2 have stationary points at x = 1.• What does the second derivative test tell you about the nature of these stationary points?• What does the first derivative test tell you about the nature of these stationary points?arrow_forwardCompute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)arrow_forwardFind the differential of the function y=√x3+4x at x=2.arrow_forward
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