Solve (7x^3)(3x^7)=

$$( 7 x ^ { 3 } ) ( 3 x ^ { 7 } ) =$$

Evaluate

$$21x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$7x^{10}\times 3$$

Multiply 7 and 3 to get 21.

$$21x^{10}$$

Differentiate w.r.t. x

$$210x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 7 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{10}\times 3)$$

Multiply 7 and 3 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(21x^{10})$$

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

$$10\times 21x^{10-1}$$

Multiply 10 times 21.

$$210x^{10-1}$$

Subtract 1 from 10.

$$210x^{9}$$