Solve 5x*(-10x^2)

$$5 x \cdot ( - 10 x ^ { 2 } )$$

Evaluate

$$-50x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$5x^{3}\left(-10\right)$$

Multiply 5 and -10 to get -50.

$$-50x^{3}$$

Differentiate w.r.t. x

$$-150x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}\left(-10\right))$$

Multiply 5 and -10 to get -50.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-50x^{3})$$

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

$$3\left(-50\right)x^{3-1}$$

Multiply 3 times -50.

$$-150x^{3-1}$$

Subtract 1 from 3.

$$-150x^{2}$$