Solve 8x^5*4x^3

$$8 x ^ { 5 } \cdot 4 x ^ { 3 }$$

Evaluate

$$32x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$8x^{8}\times 4$$

Multiply 8 and 4 to get 32.

$$32x^{8}$$

Differentiate w.r.t. x

$$256x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{8}\times 4)$$

Multiply 8 and 4 to get 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{8})$$

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

$$8\times 32x^{8-1}$$

Multiply 8 times 32.

$$256x^{8-1}$$

Subtract 1 from 8.

$$256x^{7}$$