Solve 3a^2*5a^2

$$3 a ^ { 2 } \times 5 a ^ { 2 }$$

Evaluate

$$15a^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$3a^{4}\times 5$$

Multiply 3 and 5 to get 15.

$$15a^{4}$$

Differentiate w.r.t. a

$$60a^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{4}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(15a^{4})$$

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

$$4\times 15a^{4-1}$$

Multiply 4 times 15.

$$60a^{4-1}$$

Subtract 1 from 4.

$$60a^{3}$$