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

1 Answer
Jim H
Oct 6, 2015

Use the product rule and the power and chain rules.

Explanation:

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.

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