Solve 17x^2(2x^5)

$$17 x ^ { 2 } ( 2 x ^ { 5 } )$$

Evaluate

$$34x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$17x^{7}\times 2$$

Multiply 17 and 2 to get 34.

$$34x^{7}$$

Differentiate w.r.t. x

$$238x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(17x^{7}\times 2)$$

Multiply 17 and 2 to get 34.

$$\frac{\mathrm{d}}{\mathrm{d}x}(34x^{7})$$

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

$$7\times 34x^{7-1}$$

Multiply 7 times 34.

$$238x^{7-1}$$

Subtract 1 from 7.

$$238x^{6}$$