Solve 3x(-5x^3)

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

Evaluate

$$-15x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$3x^{4}\left(-5\right)$$

Multiply 3 and -5 to get -15.

$$-15x^{4}$$

Differentiate w.r.t. x

$$-60x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{4}\left(-5\right))$$

Multiply 3 and -5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{4})$$

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

$$4\left(-15\right)x^{4-1}$$

Multiply 4 times -15.

$$-60x^{4-1}$$

Subtract 1 from 4.

$$-60x^{3}$$