Solve 3adiv12a^3

$$3 a \div 12 a ^ { 3 }$$

Evaluate

$$\frac{a^{4}}{4}$$

Solution Steps

Divide 3a by 12 to get \frac{1}{4}a.

$$\frac{1}{4}aa^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{1}{4}a^{4}$$

Differentiate w.r.t. a

$$a^{3}$$

Steps Using Definition of a Derivative

Divide 3a by 12 to get \frac{1}{4}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{4}aa^{3})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{4}a^{4})$$

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

$$4\times \frac{1}{4}a^{4-1}$$

Multiply 4 times \frac{1}{4}.

$$a^{4-1}$$

Subtract 1 from 4.

$$a^{3}$$