Solve 5a^2+3a^3+1

$$5 a ^ { 2 } + 3 a ^ { 3 } + 1$$

Differentiate w.r.t. a

$$a\left(9a+10\right)$$

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}.

$$2\times 5a^{2-1}+3\times 3a^{3-1}$$

Multiply 2 times 5.

$$10a^{2-1}+3\times 3a^{3-1}$$

Subtract 1 from 2.

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

Multiply 3 times 3.

$$10a^{1}+9a^{3-1}$$

Subtract 1 from 3.

$$10a^{1}+9a^{2}$$

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

$$10a+9a^{2}$$

Evaluate

$$3a^{3}+5a^{2}+1$$