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

Question

2306 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-06T16:13:04

Use the product rule and the power and chain rules.

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

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

So $d/dx(sqrtu) = 1/(2sqrtu) d/dx(u)$ .

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

Now use the product rule to finish.

How do you find the derivative of 4x^2 * sqrt(6x^(4)+11)4x^2 * sqrt(6x^(4)+11)?