Solve (0,2x+sqrt{7})(0,2x-sqrt{7})

$$( 0,2 x + \sqrt { 7 } ) ( 0,2 x - \sqrt { 7 } )$$

Evaluate

$$\frac{x^{2}}{25}-7$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(0,2x\right)^{2}-\left(\sqrt{7}\right)^{2}$$

Expand \left(0,2x\right)^{2}.

$$0,2^{2}x^{2}-\left(\sqrt{7}\right)^{2}$$

Calculate 0,2 to the power of 2 and get 0,04.

$$0,04x^{2}-\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$0,04x^{2}-7$$

Differentiate w.r.t. x

$$\frac{2x}{25}$$

Steps Using Derivative Rule for Sum

Consider \left(0,2x+\sqrt{7}\right)\left(0,2x-\sqrt{7}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(0,2x\right)^{2}-\left(\sqrt{7}\right)^{2})$$

Expand \left(0,2x\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0,2^{2}x^{2}-\left(\sqrt{7}\right)^{2})$$

Calculate 0,2 to the power of 2 and get 0,04.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0,04x^{2}-\left(\sqrt{7}\right)^{2})$$

The square of \sqrt{7} is 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0,04x^{2}-7)$$

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}.

$$2\times 0,04x^{2-1}$$

Multiply 2 times 0,04.

$$0,08x^{2-1}$$

Subtract 1 from 2.

$$0,08x^{1}$$

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

$$0,08x$$