5. Evaluate the following derivatives. You do not have to simplify your final answer. (a) (6 points) $\frac{d}{dx}((x^4+9)^5+1)^3$ (b) (6 points) $\frac{d}{dx}(x^33^{x^2+4})$

          5. Evaluate the following derivatives. You do not have to simplify your final answer.
(a) (6 points) $\frac{d}{dx}((x^4+9)^5+1)^3$
(b) (6 points) $\frac{d}{dx}(x^33^{x^2+4})$

5. Evaluate the following derivatives. You do not have to simplify your final answer.
(a) (6 points) (d)/(dx)((x^4+9)^5+1)^3
(b) (6 points) (d)/(dx)(x^33^x^2+4)

Added by Alexander M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nick Johnson

05/17/2023

Step 1

We use the chain rule to find $\frac{dy}{dx}$. Let $u = (x^4+9)^5+1$. Then $y = u^3$. $\frac{dy}{du} = 3u^2 = 3((x^4+9)^5+1)^2$ To find $\frac{du}{dx}$, we use the chain rule again. Let $v = x^4+9$. Then $u = v^5+1$. $\frac{du}{dv} = 5v^4 = Show more…

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5. Evaluate the following derivatives. You do not have to simplify your final answer. (a) (6 points) $\frac{d}{dx}((x^4+9)^5+1)^3$ (b) (6 points) $\frac{d}{dx}(x^3 3^{x^2+4})$