Solve 2a^50div2a^2

$$2 a ^ { 50 } \div 2 a ^ { 2 }$$

Evaluate

$$a^{52}$$

Solution Steps

Cancel out 2 and 2.

$$a^{50}a^{2}$$

To multiply powers of the same base, add their exponents. Add 50 and 2 to get 52.

$$a^{52}$$

Differentiate w.r.t. a

$$52a^{51}$$

Steps Using Definition of a Derivative

Cancel out 2 and 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{50}a^{2})$$

To multiply powers of the same base, add their exponents. Add 50 and 2 to get 52.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{52})$$

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

$$52a^{52-1}$$

Subtract 1 from 52.

$$52a^{51}$$