How do you find the derivative of $4 x^{2} \cdot \sqrt{6 x^{4} + 11}$ $4x^2 * sqrt(6x^(4)+11)$ ?

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How do you find the derivative of $4 x^{2} \cdot \sqrt{6 x^{4} + 11}$ $4x^2 * sqrt(6x^(4)+11)$ ?

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Answer 1 · 2015-10-06T16:13:04

Use the product rule and the power and chain rules.

Explanation:

The derivative of $4 x^{2}$ $4x^2$ is $8 x$ $8x$ .

Because the square root comes up often, it is worth memorizing (at some point) that $\frac{d}{d x} (\sqrt{x}) = \frac{1}{2 \sqrt{x}}$ $d/dx(sqrtx) = 1/(2sqrtx)$ .

So $\frac{d}{d x} (\sqrt{u}) = \frac{1}{2 \sqrt{u}} \frac{d}{d x} (u)$ $d/dx(sqrtu) = 1/(2sqrtu) d/dx(u)$ .

Therefore, $\frac{d}{d x} (\sqrt{6 x^{4} + 11}) = \frac{1}{2 \sqrt{6 x^{4} + 11}} (24 x^{3}) = \frac{12 x^{3}}{\sqrt{6 x^{4} + 11}}$ $d/dx(sqrt(6x^4+11)) = 1/(2sqrt(6x^4+11)) (24x^3) = (12x^3)/sqrt(6x^4+11)$

Now use the product rule to finish.

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How do you find the derivative of $4 x^{2} \cdot \sqrt{6 x^{4} + 11}$ $4x^2 * sqrt(6x^(4)+11)$ ?

1 Answer

Explanation:

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How do you find the derivative of $4 x^{2} \cdot \sqrt{6 x^{4} + 11}$ $4x^2 * sqrt(6x^(4)+11)$ ?