Solve 5a^2*2a=

$$5 a ^ { 2 } \cdot 2 a =$$

Evaluate

$$10a^{3}$$

Solution Steps

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

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

Multiply 5 and 2 to get 10.

$$10a^{3}$$

Differentiate w.r.t. a

$$30a^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a^{3}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a^{3})$$

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

$$3\times 10a^{3-1}$$

Multiply 3 times 10.

$$30a^{3-1}$$

Subtract 1 from 3.

$$30a^{2}$$