Solve sqrt[3]{8^2}x

$$\sqrt[ 3 ] { 8 ^ { 2 } } x$$

Evaluate

$$4x$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt[3]{64}x$$

Calculate \sqrt[3]{64} and get 4.

$$4x$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Calculate 8 to the power of 2 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt[3]{64}x)$$

Calculate \sqrt[3]{64} and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x)$$

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

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

For any term t except 0, t^{0}=1.

$$4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4$$