Solve -x*x^6*x*x

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

Evaluate

$$-x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

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

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\left(-x\right)x^{8}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$-x^{9}$$

Differentiate w.r.t. x

$$-9x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

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

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)x^{8})$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

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

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.

$$-9x^{8}$$