Calculate the derivative of the following functions. Use the rules for derivatives. a. w(x) = x² + b. v(x) = ex c. s(x) = x³e™ d. q(x) = - f. q(x) = 20 7x³ - 1 X x² - 2 X 1 e. q(x)= tan¯¹(x²) COS X x² + 1 g. f(x)=x sec(2³) h. v(x) = log5 (xª + 1) i. s(x) = 102³ _j. q(x) = tan² x + ✔x5 + 3 2√x²
Calculate the derivative of the following functions. Use the rules for derivatives. a. w(x) = x² + b. v(x) = ex c. s(x) = x³e™ d. q(x) = - f. q(x) = 20 7x³ - 1 X x² - 2 X 1 e. q(x)= tan¯¹(x²) COS X x² + 1 g. f(x)=x sec(2³) h. v(x) = log5 (xª + 1) i. s(x) = 102³ _j. q(x) = tan² x + ✔x5 + 3 2√x²
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Calculate the derivative of the following functions. Use the rules for derivatives.
a. \( w(x) = x^4 + \frac{20}{7x^3} + \sqrt[4]{x^5} + \frac{3}{2\sqrt{x^2}} \)
b. \( v(x) = e^x - \frac{1}{x} \)
c. \( s(x) = x^3 e^x \)
d. \( q(x) = \frac{x^2 - 2}{x - 1} \)
e. \( q(x) = \tan^{-1}(x^2) \)
f. \( q(x) = \frac{\cos x}{x^2 + 1} \)
g. \( f(x) = x \sec(x^3) \)
h. \( v(x) = \log_5(x^4 + 1) \)
i. \( s(x) = 10^{x^3} \)
j. \( q(x) = \tan^2 x \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb11ca76e-99cc-49cc-ab47-e18e3e84e4f7%2Fc78d006b-f96c-480f-ad12-a66e802e25f3%2Fb118nhd_processed.png&w=3840&q=75)
Transcribed Image Text:Calculate the derivative of the following functions. Use the rules for derivatives.
a. \( w(x) = x^4 + \frac{20}{7x^3} + \sqrt[4]{x^5} + \frac{3}{2\sqrt{x^2}} \)
b. \( v(x) = e^x - \frac{1}{x} \)
c. \( s(x) = x^3 e^x \)
d. \( q(x) = \frac{x^2 - 2}{x - 1} \)
e. \( q(x) = \tan^{-1}(x^2) \)
f. \( q(x) = \frac{\cos x}{x^2 + 1} \)
g. \( f(x) = x \sec(x^3) \)
h. \( v(x) = \log_5(x^4 + 1) \)
i. \( s(x) = 10^{x^3} \)
j. \( q(x) = \tan^2 x \)
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