Find the first partial derivatives of the function fxtarctan

Find the first partial derivatives of the function.
f(x,t)=arctan(x(t)^1/2)

fx(x,t)=?
fy(x,t)=?

d/dt(arctan(x(t)^1/2) = (x\'(t))/(sqrt(x(t)) (2 x(t)+2))

fx(x,t)= 1/2[x(t)(1+x(t)²)

fy(x,t)=0

$Find the first partial derivatives of the function. f(x,t)=arctan(x(t)^1/2) fx(x,t)=? fy(x,t)=?Solutiond/dt(arctan(x(t)^1/2) = (x\'(t))/(sqrt(x(t)) (2 x(t)+2))$

Find the first partial derivatives of the function fxtarctan

Solution

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