Solve 4^3sqrt{24}x^3

$$4 ^ { 3 } \sqrt { 24 } x ^ { 3 }$$

Evaluate

$$128\sqrt{6}x^{3}$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$64\sqrt{24}x^{3}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$64\times 2\sqrt{6}x^{3}$$

Multiply 64 and 2 to get 128.

$$128\sqrt{6}x^{3}$$

Differentiate w.r.t. x

$$384\sqrt{6}x^{2}$$