Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.1 - Derivatives of Polynomials and Exponential Functions - 3.1 Exercises: 45

Answer

- First derivative: $$f'(x)=0.005x^4-0.06x^2$$ - Second derivative: $$f''(x)=0.02x^3-0.12x$$

Work Step by Step

$$f(x)=0.001x^5-0.02x^3$$ - First derivative: $$f'(x)=0.001\frac{d}{dx}(x^5)-0.02\frac{d}{dx}(x^3)$$ $$f'(x)=0.001\times5x^4-0.02\times3x^2$$ $$f'(x)=0.005x^4-0.06x^2$$ - Second derivative: $$f''(x)=0.005\frac{d}{dx}(x^4)-0.06\frac{d}{dx}(x^2)$$ $$f''(x)=0.005\times4x^3-0.06\times2x$$ $$f''(x)=0.02x^3-0.12x$$
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