Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 43

Answer

The derivative is $8x+3$.

Work Step by Step

To start solving this problem you must first split the numerator. A note worth mentioning is that $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$ but $\frac{a}{b+c}\ne\frac{a}{b}+\frac{a}{c}$. Keeping this straight would help you avoid making mistakes and simplifying calculations. By splitting we get $y = \frac{4x^3}{x}+\frac{3x^2}{x} = 4x^2+3x$. To differentiate, just differentiate the individual terms using the power rule $((x^n)' = nx^{n-1})$. The derivative of $4x^2$ is $8x$ while the derivative of $3x$ is $3$. This gives us $y' = 8x+3$.
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