Solve 8x^6*(-5x)

$$8 x ^ { 6 } \cdot ( - 5 x )$$

Evaluate

$$-40x^{7}$$

Solution Steps

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

$$8x^{7}\left(-5\right)$$

Multiply 8 and -5 to get -40.

$$-40x^{7}$$

Differentiate w.r.t. x

$$-280x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{7}\left(-5\right))$$

Multiply 8 and -5 to get -40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-40x^{7})$$

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

$$7\left(-40\right)x^{7-1}$$

Multiply 7 times -40.

$$-280x^{7-1}$$

Subtract 1 from 7.

$$-280x^{6}$$