Solve (4h^-1)(3h^4)

$$( 4 h ^ { - 1 } ) ( 3 h ^ { 4 } )$$

Evaluate

$$12h^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and 4 to get 3.

$$4h^{3}\times 3$$

Multiply 4 and 3 to get 12.

$$12h^{3}$$

Differentiate w.r.t. h

$$36h^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -1 and 4 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}h}(4h^{3}\times 3)$$

Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}h}(12h^{3})$$

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

$$3\times 12h^{3-1}$$

Multiply 3 times 12.

$$36h^{3-1}$$

Subtract 1 from 3.

$$36h^{2}$$