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Differentiate w.r.t. x
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\left(\sqrt{x}\right)^{2}-\left(2\sqrt{5}\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
x-\left(2\sqrt{5}\right)^{2}
Calculate \sqrt{x} to the power of 2 and get x.
x-2^{2}\left(\sqrt{5}\right)^{2}
Expand \left(2\sqrt{5}\right)^{2}.
x-4\left(\sqrt{5}\right)^{2}
Calculate 2 to the power of 2 and get 4.
x-4\times 5
The square of \sqrt{5} is 5.
x-20
Multiply 4 and 5 to get 20.
\frac{\mathrm{d}}{\mathrm{d}x}(\left(\sqrt{x}\right)^{2}-\left(2\sqrt{5}\right)^{2})
Consider \left(\sqrt{x}+2\sqrt{5}\right)\left(\sqrt{x}-2\sqrt{5}\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}(x-\left(2\sqrt{5}\right)^{2})
Calculate \sqrt{x} to the power of 2 and get x.
\frac{\mathrm{d}}{\mathrm{d}x}(x-2^{2}\left(\sqrt{5}\right)^{2})
Expand \left(2\sqrt{5}\right)^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(x-4\left(\sqrt{5}\right)^{2})
Calculate 2 to the power of 2 and get 4.
\frac{\mathrm{d}}{\mathrm{d}x}(x-4\times 5)
The square of \sqrt{5} is 5.
\frac{\mathrm{d}}{\mathrm{d}x}(x-20)
Multiply 4 and 5 to get 20.
x^{1-1}
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}.
x^{0}
Subtract 1 from 1.
1
For any term t except 0, t^{0}=1.