Solve 5a^25a

$$5 a ^ { 2 } 5 a$$

Evaluate

$$25a^{3}$$

Solution Steps

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

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

Multiply 5 and 5 to get 25.

$$25a^{3}$$

Differentiate w.r.t. a

$$75a^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}a}(25a^{3})$$

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

$$3\times 25a^{3-1}$$

Multiply 3 times 25.

$$75a^{3-1}$$

Subtract 1 from 3.

$$75a^{2}$$