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

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

Evaluate

$$-12x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$3x^{8}\left(-4\right)$$

Multiply 3 and -4 to get -12.

$$-12x^{8}$$

Differentiate w.r.t. x

$$-96x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{8}\left(-4\right))$$

Multiply 3 and -4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{8})$$

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

$$8\left(-12\right)x^{8-1}$$

Multiply 8 times -12.

$$-96x^{8-1}$$

Subtract 1 from 8.

$$-96x^{7}$$