Solve 5x^7*8x

$$5 x ^ { 7 } \cdot 8 x$$

Evaluate

$$40x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$5x^{8}\times 8$$

Multiply 5 and 8 to get 40.

$$40x^{8}$$

Differentiate w.r.t. x

$$320x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{8}\times 8)$$

Multiply 5 and 8 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(40x^{8})$$

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

$$8\times 40x^{8-1}$$

Multiply 8 times 40.

$$320x^{8-1}$$

Subtract 1 from 8.

$$320x^{7}$$