What is the derivative of sqrt((x+39^2+(43+x)^2)) ?

The derivative of sqrt((x+39^2+(43+x)^2)) is (2(x+41))/(sqrt(2x^2+164x+3370))

What is the first derivative of sqrt((x+39^2+(43+x)^2)) ?

The first derivative of sqrt((x+39^2+(43+x)^2)) is (2(x+41))/(sqrt(2x^2+164x+3370))

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\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

\frac{2 ( x + 41 )}{2 x ^{2} + 164 x + 3370}

Solution steps

\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

Apply the chain rule:

\frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} \frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

= \frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} \frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2})

\frac{d}{d x} ((x + 39)^{2} + (43 + x)^{2}) = 4 x + 164

= \frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} (4 x + 164)

Simplify

\frac{1}{2 ( x + 39 ) ^{2} + ( 43 + x ) ^{2}} (4 x + 164) : \frac{2 ( x + 41 )}{2 x ^{2} + 164 x + 3370}

= \frac{2 ( x + 41 )}{2 x ^{2} + 164 x + 3370}

What is the derivative of sqrt((x+39^2+(43+x)^2)) ?
The derivative of sqrt((x+39^2+(43+x)^2)) is (2(x+41))/(sqrt(2x^2+164x+3370))
What is the first derivative of sqrt((x+39^2+(43+x)^2)) ?
The first derivative of sqrt((x+39^2+(43+x)^2)) is (2(x+41))/(sqrt(2x^2+164x+3370))