Solve 5x^-8*2x^5=

$$5 x ^ { - 8 } \times 2 x ^ { 5 } =$$

Evaluate

$$\frac{10}{x^{3}}$$

Solution Steps

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

$$5x^{-3}\times 2$$

Multiply 5 and 2 to get 10.

$$10x^{-3}$$

Differentiate w.r.t. x

$$-\frac{30}{x^{4}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{-3}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{-3})$$

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

$$-3\times 10x^{-3-1}$$

Multiply -3 times 10.

$$-30x^{-3-1}$$

Subtract 1 from -3.

$$-30x^{-4}$$