Solve (-3x^3)*(5x^4)

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

Evaluate

$$-15x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$-3x^{7}\times 5$$

Multiply -3 and 5 to get -15.

$$-15x^{7}$$

Differentiate w.r.t. x

$$-105x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{7}\times 5)$$

Multiply -3 and 5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-15x^{7})$$

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

$$7\left(-15\right)x^{7-1}$$

Multiply 7 times -15.

$$-105x^{7-1}$$

Subtract 1 from 7.

$$-105x^{6}$$