Solve 27x^3-8

$$27 { x }^{ 3-8 }$$

Differentiate w.r.t. x

$$-\frac{135}{x^{6}}$$

Steps Using Definition of a Derivative

Subtract 8 from 3 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{-5})$$

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

$$-5\times 27x^{-5-1}$$

Multiply -5 times 27.

$$-135x^{-5-1}$$

Subtract 1 from -5.

$$-135x^{-6}$$

Evaluate

$$\frac{27}{x^{5}}$$

Solution Steps

Subtract 8 from 3 to get -5.

$$27x^{-5}$$