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

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

Differentiate w.r.t. a

$$a\left(2v+5a^{3}-3a\right)$$

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}.

$$5a^{5-1}+3\left(-1\right)a^{3-1}+2va^{2-1}$$

Subtract 1 from 5.

$$5a^{4}+3\left(-1\right)a^{3-1}+2va^{2-1}$$

Multiply 3 times -1.

$$5a^{4}-3a^{3-1}+2va^{2-1}$$

Subtract 1 from 3.

$$5a^{4}-3a^{2}+2va^{2-1}$$

Subtract 1 from 2.

$$5a^{4}-3a^{2}+2va^{1}$$

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

$$5a^{4}-3a^{2}+2va$$

Evaluate

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