Solve 3x^3*(-3x^2)

$$3 x ^ { 3 } \cdot ( - 3 x ^ { 2 } )$$

Evaluate

$$-9x^{5}$$

Solution Steps

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

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

Multiply 3 and -3 to get -9.

$$-9x^{5}$$

Differentiate w.r.t. x

$$-45x^{4}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and -3 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{5})$$

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

$$5\left(-9\right)x^{5-1}$$

Multiply 5 times -9.

$$-45x^{5-1}$$

Subtract 1 from 5.

$$-45x^{4}$$