Solve 3^4-x^2+1

$$3 ^ { 4 } - x ^ { 2 } + 1$$

Evaluate

$$82-x^{2}$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$81-x^{2}+1$$

Add 81 and 1 to get 82.

$$82-x^{2}$$

Differentiate w.r.t. x

$$-2x$$

Steps Using Derivative Rule for Sum

Calculate 3 to the power of 4 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(81-x^{2}+1)$$

Add 81 and 1 to get 82.

$$\frac{\mathrm{d}}{\mathrm{d}x}(82-x^{2})$$

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}.

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

Multiply 2 times -1.

$$-2x^{2-1}$$

Subtract 1 from 2.

$$-2x^{1}$$

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

$$-2x$$