Solve 4^4-y^2+4-1=

$$4 ^ { 4 } - y ^ { 2 } + 4 - 1 =$$

Evaluate

$$259-y^{2}$$

Solution Steps

Calculate 4 to the power of 4 and get 256.

$$256-y^{2}+4-1$$

Add 256 and 4 to get 260.

$$260-y^{2}-1$$

Subtract 1 from 260 to get 259.

$$259-y^{2}$$

Differentiate w.r.t. y

$$-2y$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 4 and get 256.

$$\frac{\mathrm{d}}{\mathrm{d}y}(256-y^{2}+4-1)$$

Add 256 and 4 to get 260.

$$\frac{\mathrm{d}}{\mathrm{d}y}(260-y^{2}-1)$$

Subtract 1 from 260 to get 259.

$$\frac{\mathrm{d}}{\mathrm{d}y}(259-y^{2})$$

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}.

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

Multiply 2 times -1.

$$-2y^{2-1}$$

Subtract 1 from 2.

$$-2y^{1}$$

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

$$-2y$$