Solve 3a*a^2+a^3=

$$3 a \cdot a ^ { 2 } + a ^ { 3 } =$$

Evaluate

$$4a^{3}$$

Solution Steps

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

$$3a^{3}+a^{3}$$

Combine 3a^{3} and a^{3} to get 4a^{3}.

$$4a^{3}$$

Differentiate w.r.t. a

$$12a^{2}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3a^{2}a^{1-1}+3a^{3-1}$$

Subtract 1 from 1.

$$3a^{2}a^{0}+3a^{3-1}$$

Subtract 1 from 3.

$$3a^{2}a^{0}+3a^{2}$$

For any term t except 0, t^{0}=1.

$$3a^{2}\times 1+3a^{2}$$

For any term t, t\times 1=t and 1t=t.

$$3a^{2}+3a^{2}$$