Solve (-x)x(-x^5)x(-x)

$$( - x ) x ( - x ^ { 5 } ) x ( - x )$$

Evaluate

$$-x^{9}$$

Solution Steps

Multiply -x and -x to get \left(-x\right)^{2}.

$$\left(-x\right)^{2}x\left(-x^{5}\right)x$$

Multiply x and x to get x^{2}.

$$\left(-x\right)^{2}x^{2}\left(-x^{5}\right)$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}x^{2}\left(-x^{5}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$x^{4}\left(-x^{5}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$x^{9}\left(-1\right)$$

Differentiate w.r.t. x

$$-9x^{8}$$

Steps Using Definition of a Derivative

Multiply -x and -x to get \left(-x\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)^{2}x\left(-x^{5}\right)x)$$

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)^{2}x^{2}\left(-x^{5}\right))$$

Calculate -x to the power of 2 and get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{2}\left(-x^{5}\right))$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\left(-x^{5}\right))$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{9}\left(-1\right))$$

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

$$9\left(-1\right)x^{9-1}$$

Multiply 9 times -1.

$$-9x^{9-1}$$

Subtract 1 from 9.

$$-9x^{8}$$