Solve 4x^6*(-x^2)

$$4 x ^ { 6 } \cdot ( - x ^ { 2 } )$$

Evaluate

$$-4x^{8}$$

Solution Steps

Multiply 4 and -1 to get -4.

$$-4x^{6}x^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$-4x^{8}$$

Differentiate w.r.t. x

$$-32x^{7}$$

Steps Using Definition of a Derivative

Multiply 4 and -1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{6}x^{2})$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{8})$$

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

$$8\left(-4\right)x^{8-1}$$

Multiply 8 times -4.

$$-32x^{8-1}$$

Subtract 1 from 8.

$$-32x^{7}$$