Solve 27x^4x^42

$$27 x ^ { 4 } x ^ { 4 } 2$$

Evaluate

$$54x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$27x^{8}\times 2$$

Multiply 27 and 2 to get 54.

$$54x^{8}$$

Differentiate w.r.t. x

$$432x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{8}\times 2)$$

Multiply 27 and 2 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(54x^{8})$$

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

$$8\times 54x^{8-1}$$

Multiply 8 times 54.

$$432x^{8-1}$$

Subtract 1 from 8.

$$432x^{7}$$