Solve 3a^3/12a^9

$$\frac{ 3 { a }^{ 3 } }{ 12 } { a }^{ 9 }$$

Evaluate

$$\frac{a^{12}}{4}$$

Solution Steps

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

$$\frac{1}{4}a^{3}a^{9}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{1}{4}a^{12}$$

Differentiate w.r.t. a

$$3a^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{4}a^{3}a^{9})$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{4}a^{12})$$

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

$$12\times \frac{1}{4}a^{12-1}$$

Multiply 12 times \frac{1}{4}.

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

Subtract 1 from 12.

$$3a^{11}$$