Solve 2a^3*5a^2

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

Evaluate

$$10a^{5}$$

Solution Steps

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

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

Multiply 2 and 5 to get 10.

$$10a^{5}$$

Differentiate w.r.t. a

$$50a^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{5}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{5})$$

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

$$5\times 10a^{5-1}$$

Multiply 5 times 10.

$$50a^{5-1}$$

Subtract 1 from 5.

$$50a^{4}$$