Solve 3x^3*12x^2=

$$3 x ^ { 3 } \cdot 12 x ^ { 2 } =$$

Evaluate

$$36x^{5}$$

Solution Steps

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

$$3x^{5}\times 12$$

Multiply 3 and 12 to get 36.

$$36x^{5}$$

Differentiate w.r.t. x

$$180x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{5}\times 12)$$

Multiply 3 and 12 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{5})$$

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

$$5\times 36x^{5-1}$$

Multiply 5 times 36.

$$180x^{5-1}$$

Subtract 1 from 5.

$$180x^{4}$$