Solve (6x^3)(7x^4)

$$(6 { x }^{ 3 } )(7 { x }^{ 4 } )$$

Evaluate

$$42x^{7}$$

Solution Steps

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

$$6x^{7}\times 7$$

Multiply 6 and 7 to get 42.

$$42x^{7}$$

Differentiate w.r.t. x

$$294x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{7}\times 7)$$

Multiply 6 and 7 to get 42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(42x^{7})$$

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

$$7\times 42x^{7-1}$$

Multiply 7 times 42.

$$294x^{7-1}$$

Subtract 1 from 7.

$$294x^{6}$$