Solve (9x^-7)(4x^3)

$$( 9 x ^ { - 7 } ) ( 4 x ^ { 3 } )$$

Evaluate

$$\frac{36}{x^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and 3 to get -4.

$$9x^{-4}\times 4$$

Multiply 9 and 4 to get 36.

$$36x^{-4}$$

Differentiate w.r.t. x

$$-\frac{144}{x^{5}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -7 and 3 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{-4}\times 4)$$

Multiply 9 and 4 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{-4})$$

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

$$-4\times 36x^{-4-1}$$

Multiply -4 times 36.

$$-144x^{-4-1}$$

Subtract 1 from -4.

$$-144x^{-5}$$