Solve (-x^3)*x^10*x

$$(- { x }^{ 3 } ) \times { x }^{ 10 } \times x$$

Evaluate

$$-x^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\left(-x^{3}\right)x^{11}$$

To multiply powers of the same base, add their exponents. Add 3 and 11 to get 14.

$$-x^{14}$$

Differentiate w.r.t. x

$$-14x^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 1 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x^{3}\right)x^{11})$$

To multiply powers of the same base, add their exponents. Add 3 and 11 to get 14.

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

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

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

Multiply 14 times -1.

$$-14x^{14-1}$$

Subtract 1 from 14.

$$-14x^{13}$$