Solve (a^2+1)+(-2+5a^2)

$$( a ^ { 2 } + 1 ) + ( - 2 + 5 a ^ { 2 } )$$

Evaluate

$$6a^{2}-1$$

Solution Steps

Subtract 2 from 1 to get -1.

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

Combine a^{2} and 5a^{2} to get 6a^{2}.

$$6a^{2}-1$$

Differentiate w.r.t. a

$$12a$$

Steps Using Derivative Rule for Sum

Subtract 2 from 1 to get -1.

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

Combine a^{2} and 5a^{2} to get 6a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{2}-1)$$

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}.

$$2\times 6a^{2-1}$$

Multiply 2 times 6.

$$12a^{2-1}$$

Subtract 1 from 2.

$$12a^{1}$$

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

$$12a$$