Solve x^3sqrt{(-4)^10}

$$x ^ { 3 } \sqrt { ( - 4 ) ^ { 10 } }$$

Evaluate

$$1024x^{3}$$

Solution Steps

Calculate -4 to the power of 10 and get 1048576.

$$x^{3}\sqrt{1048576}$$

Calculate the square root of 1048576 and get 1024.

$$x^{3}\times 1024$$

Differentiate w.r.t. x

$$3072x^{2}$$

Steps Using Definition of a Derivative

Calculate -4 to the power of 10 and get 1048576.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\sqrt{1048576})$$

Calculate the square root of 1048576 and get 1024.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 1024)$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 1024x^{3-1}$$

Multiply 3 times 1024.

$$3072x^{3-1}$$

Subtract 1 from 3.

$$3072x^{2}$$