Solve -2x^7*5x^-2

$$- 2 x ^ { 7 } \cdot 5 x ^ { - 2 }$$

Evaluate

$$-10x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and -2 to get 5.

$$-2x^{5}\times 5$$

Multiply -2 and 5 to get -10.

$$-10x^{5}$$

Differentiate w.r.t. x

$$-50x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and -2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{5}\times 5)$$

Multiply -2 and 5 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-10x^{5})$$

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

$$5\left(-10\right)x^{5-1}$$

Multiply 5 times -10.

$$-50x^{5-1}$$

Subtract 1 from 5.

$$-50x^{4}$$