Solve 5^2+7^2-x^2

$$5 ^ { 2 } + 7 ^ { 2 } - x ^ { 2 }$$

Evaluate

$$74-x^{2}$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25+7^{2}-x^{2}$$

Calculate 7 to the power of 2 and get 49.

$$25+49-x^{2}$$

Add 25 and 49 to get 74.

$$74-x^{2}$$

Differentiate w.r.t. x

$$-2x$$

Steps Using Derivative Rule for Sum

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25+7^{2}-x^{2})$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25+49-x^{2})$$

Add 25 and 49 to get 74.

$$\frac{\mathrm{d}}{\mathrm{d}x}(74-x^{2})$$

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.

$$-2x$$