Solve -x^2*x*x^3=

$$- x ^ { 2 } \cdot x \cdot x ^ { 3 } =$$

Evaluate

$$-x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(-x^{2}\right)x^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-x^{6}$$

Differentiate w.r.t. x

$$-6x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x^{2}\right)x^{4})$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{6})$$

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

$$6\left(-1\right)x^{6-1}$$

Multiply 6 times -1.

$$-6x^{6-1}$$

Subtract 1 from 6.

$$-6x^{5}$$