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Differentiate w.r.t. x
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3x^{2}+2x\sqrt{2}+3\sqrt{2}x+2\left(\sqrt{2}\right)^{2}
Apply the distributive property by multiplying each term of x+\sqrt{2} by each term of 3x+2\sqrt{2}.
3x^{2}+5x\sqrt{2}+2\left(\sqrt{2}\right)^{2}
Combine 2x\sqrt{2} and 3\sqrt{2}x to get 5x\sqrt{2}.
3x^{2}+5x\sqrt{2}+2\times 2
The square of \sqrt{2} is 2.
3x^{2}+5x\sqrt{2}+4
Multiply 2 and 2 to get 4.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+2x\sqrt{2}+3\sqrt{2}x+2\left(\sqrt{2}\right)^{2})
Apply the distributive property by multiplying each term of x+\sqrt{2} by each term of 3x+2\sqrt{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+5x\sqrt{2}+2\left(\sqrt{2}\right)^{2})
Combine 2x\sqrt{2} and 3\sqrt{2}x to get 5x\sqrt{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+5x\sqrt{2}+2\times 2)
The square of \sqrt{2} is 2.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+5x\sqrt{2}+4)
Multiply 2 and 2 to get 4.
2\times 3x^{2-1}+5\sqrt{2}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}.
6x^{2-1}+5\sqrt{2}x^{1-1}
Multiply 2 times 3.
6x^{1}+5\sqrt{2}x^{1-1}
Subtract 1 from 2.
6x^{1}+5\sqrt{2}x^{0}
Subtract 1 from 1.
6x+5\sqrt{2}x^{0}
For any term t, t^{1}=t.
6x+5\sqrt{2}\times 1
For any term t except 0, t^{0}=1.
6x+5\sqrt{2}
For any term t, t\times 1=t and 1t=t.