Solve (2h^-3)(3h^-3)

$$( 2 h ^ { - 3 } ) ( 3 h ^ { - 3 } )$$

Evaluate

$$\frac{6}{h^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

$$2h^{-6}\times 3$$

Multiply 2 and 3 to get 6.

$$6h^{-6}$$

Differentiate w.r.t. h

$$-\frac{36}{h^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}h}(2h^{-6}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}h}(6h^{-6})$$

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

$$-6\times 6h^{-6-1}$$

Multiply -6 times 6.

$$-36h^{-6-1}$$

Subtract 1 from -6.

$$-36h^{-7}$$