What is (\partial)/(\partial x)(e^{(x-1)^2}cos(y)) ?

The answer to (\partial)/(\partial x)(e^{(x-1)^2}cos(y)) is cos(y)e^{(x-1)^2}*2(x-1)

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(\partial)/(\partial x)(e^{(x-1)^2}cos(y))

\frac{\partial}{\partial x} (e^{(x - 1)^{2}} cos (y))

cos (y) e^{(x - 1)^{2}} \cdot 2 (x - 1)

Solution steps

\frac{\partial}{\partial x} (e^{(x - 1)^{2}} cos (y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= cos (y) \frac{\partial}{\partial x} (e^{(x - 1)^{2}})

Apply the chain rule:

e^{(x - 1)^{2}} \frac{\partial}{\partial x} ((x - 1)^{2})

= e^{(x - 1)^{2}} \frac{\partial}{\partial x} ((x - 1)^{2})

\frac{\partial}{\partial x} ((x - 1)^{2}) = 2 (x - 1)

= cos (y) e^{(x - 1)^{2}} \cdot 2 (x - 1)

x \to 0 + lim (\frac{7}{x ^{3} - 2 x ^{2}})

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What is (\partial)/(\partial x)(e^{(x-1)^2}cos(y)) ?
The answer to (\partial)/(\partial x)(e^{(x-1)^2}cos(y)) is cos(y)e^{(x-1)^2}*2(x-1)