Solve 125a^2*29a^3

$$125 a ^ { 2 } \cdot 29 a ^ { 3 }$$

Evaluate

$$3625a^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$125a^{5}\times 29$$

Multiply 125 and 29 to get 3625.

$$3625a^{5}$$

Differentiate w.r.t. a

$$18125a^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(125a^{5}\times 29)$$

Multiply 125 and 29 to get 3625.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3625a^{5})$$

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

$$5\times 3625a^{5-1}$$

Multiply 5 times 3625.

$$18125a^{5-1}$$

Subtract 1 from 5.

$$18125a^{4}$$