Solve 25^2*20^2+x^2

$$25 ^ { 2 } \cdot 20 ^ { 2 } + x ^ { 2 }$$

Evaluate

$$x^{2}+250000$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$625\times 20^{2}+x^{2}$$

Calculate 20 to the power of 2 and get 400.

$$625\times 400+x^{2}$$

Multiply 625 and 400 to get 250000.

$$250000+x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Derivative Rule for Sum

Calculate 25 to the power of 2 and get 625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(625\times 20^{2}+x^{2})$$

Calculate 20 to the power of 2 and get 400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(625\times 400+x^{2})$$

Multiply 625 and 400 to get 250000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(250000+x^{2})$$

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}.

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

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$