Solve 3a*4a^2=

$$3 a \cdot 4 a ^ { 2 } =$$

Evaluate

$$12a^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$3a^{3}\times 4$$

Multiply 3 and 4 to get 12.

$$12a^{3}$$

Differentiate w.r.t. a

$$36a^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{3}\times 4)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(12a^{3})$$

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

$$3\times 12a^{3-1}$$

Multiply 3 times 12.

$$36a^{3-1}$$

Subtract 1 from 3.

$$36a^{2}$$