Solve 5^2+(2*5^2+x^2)+x

$$5 ^ { 2 } + ( 2 \times 5 ^ { 2 } + x ^ { 2 } ) + x$$

Evaluate

$$x^{2}+x+75$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25+2\times 5^{2}+x^{2}+x$$

Calculate 5 to the power of 2 and get 25.

$$25+2\times 25+x^{2}+x$$

Multiply 2 and 25 to get 50.

$$25+50+x^{2}+x$$

Add 25 and 50 to get 75.

$$75+x^{2}+x$$

Differentiate w.r.t. x

$$2x+1$$

Steps Using Derivative Rule for Sum

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25+2\times 5^{2}+x^{2}+x)$$

Calculate 5 to the power of 2 and get 25.

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

Multiply 2 and 25 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25+50+x^{2}+x)$$

Add 25 and 50 to get 75.

$$\frac{\mathrm{d}}{\mathrm{d}x}(75+x^{2}+x)$$

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}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$2x^{1}+x^{0}$$

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

$$2x+x^{0}$$

For any term t except 0, t^{0}=1.

$$2x+1$$