Solve 12a^2-22a+5a^3+1-a

$$12 a ^ { 2 } - 22 a + 5 a ^ { 3 } + 1 - a$$

Differentiate w.r.t. a

$$15a^{2}+24a-23$$

Steps Using Derivative Rule for Sum

Combine -22a and -a to get -23a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(12a^{2}-23a+5a^{3}+1)$$

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}.

$$2\times 12a^{2-1}-23a^{1-1}+3\times 5a^{3-1}$$

Multiply 2 times 12.

$$24a^{2-1}-23a^{1-1}+3\times 5a^{3-1}$$

Subtract 1 from 2.

$$24a^{1}-23a^{1-1}+3\times 5a^{3-1}$$

Subtract 1 from 1.

$$24a^{1}-23a^{0}+3\times 5a^{3-1}$$

Multiply 1 times -23.

$$24a^{1}-23a^{0}+15a^{3-1}$$

Subtract 1 from 3.

$$24a^{1}-23a^{0}+15a^{2}$$

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

$$24a-23a^{0}+15a^{2}$$

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

$$24a-23+15a^{2}$$

Evaluate

$$5a^{3}+12a^{2}-23a+1$$

Solution Steps

Combine -22a and -a to get -23a.

$$12a^{2}-23a+5a^{3}+1$$