Solve 7x(-2x^9)

$$7x(-2 { x }^{ 9 } )$$

Evaluate

$$-14x^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$7x^{10}\left(-2\right)$$

Multiply 7 and -2 to get -14.

$$-14x^{10}$$

Differentiate w.r.t. x

$$-140x^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{10}\left(-2\right))$$

Multiply 7 and -2 to get -14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-14x^{10})$$

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

$$10\left(-14\right)x^{10-1}$$

Multiply 10 times -14.

$$-140x^{10-1}$$

Subtract 1 from 10.

$$-140x^{9}$$