Solve 91a^2+2a+5a+10

$$91 a ^ { 2 } + 2 a + 5 a + 10$$

Differentiate w.r.t. a

$$182a+7$$

Steps Using Derivative Rule for Sum

Combine 2a and 5a to get 7a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(91a^{2}+7a+10)$$

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}.

$$2\times 91a^{2-1}+7a^{1-1}$$

Multiply 2 times 91.

$$182a^{2-1}+7a^{1-1}$$

Subtract 1 from 2.

$$182a^{1}+7a^{1-1}$$

Subtract 1 from 1.

$$182a^{1}+7a^{0}$$

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

$$182a+7a^{0}$$

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

$$182a+7\times 1$$

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

$$182a+7$$

Evaluate

$$91a^{2}+7a+10$$

Solution Steps

Combine 2a and 5a to get 7a.

$$91a^{2}+7a+10$$