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

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

Evaluate

$$6-a^{2}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$1-a^{2}+4+1$$

Add 1 and 4 to get 5.

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

Add 5 and 1 to get 6.

$$6-a^{2}$$

Differentiate w.r.t. a

$$-2a$$

Steps Using Derivative Rule for Sum

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(1-a^{2}+4+1)$$

Add 1 and 4 to get 5.

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

Add 5 and 1 to get 6.

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

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}.

$$2\left(-1\right)a^{2-1}$$

Multiply 2 times -1.

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

Subtract 1 from 2.

$$-2a^{1}$$

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

$$-2a$$