Solve (-2x^3)(-5x^2)=

$$( - 2 x ^ { 3 } ) ( - 5 x ^ { 2 } ) =$$

Evaluate

$$10x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-2x^{5}\left(-5\right)$$

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 3 and 2 to get 5.

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

Multiply -2 and -5 to get 10.

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

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

$$5\times 10x^{5-1}$$

Multiply 5 times 10.

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

Subtract 1 from 5.

$$50x^{4}$$