Solve (-4x^-2)(9x^9)

$$( - 4 x ^ { - 2 } ) ( 9 x ^ { 9 } )$$

Evaluate

$$-36x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 9 to get 7.

$$-4x^{7}\times 9$$

Multiply -4 and 9 to get -36.

$$-36x^{7}$$

Differentiate w.r.t. x

$$-252x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -2 and 9 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{7}\times 9)$$

Multiply -4 and 9 to get -36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-36x^{7})$$

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

$$7\left(-36\right)x^{7-1}$$

Multiply 7 times -36.

$$-252x^{7-1}$$

Subtract 1 from 7.

$$-252x^{6}$$