Solve (4(1/4x^3))^1/3

$$( 4 ( \frac { 1 } { 4 } x ^ { 3 } ) ) ^ { 1 / 3 }$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Multiply 4 and \frac{1}{4} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{3}\right)^{\frac{1}{3}})$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{1}{3} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})$$

Calculate x to the power of 1 and get x.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$

Evaluate

$$x$$

Solution Steps

Multiply 4 and \frac{1}{4} to get 1.

$$\left(x^{3}\right)^{\frac{1}{3}}$$