What is (\partial)/(\partial y)(e^xsec^2(y)) ?

The answer to (\partial)/(\partial y)(e^xsec^2(y)) is 2e^xsec^2(y)tan(y)

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(\partial)/(\partial y)(e^xsec^2(y))

\frac{\partial}{\partial y} (e^{x} sec^{2} (y))

2 e^{x} sec^{2} (y) tan (y)

Solution steps

\frac{\partial}{\partial y} (e^{x} sec^{2} (y))

Treat

x

as a constant

Take the constant out:

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

= e^{x} \frac{\partial}{\partial y} (sec^{2} (y))

Apply the chain rule:

2 sec (y) \frac{\partial}{\partial y} (sec (y))

= 2 sec (y) \frac{\partial}{\partial y} (sec (y))

\frac{\partial}{\partial y} (sec (y)) = sec (y) tan (y)

= e^{x} \cdot 2 sec (y) sec (y) tan (y)

Simplify

e^{x} \cdot 2 sec (y) sec (y) tan (y) : 2 e^{x} sec^{2} (y) tan (y)

= 2 e^{x} sec^{2} (y) tan (y)

f (x) = x^{2} - 8, (4, 8)

y = 9 x - 6 x, (1, 3)

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\int sin (x^{2}) + cos (2 x) - \frac{1}{2} d x

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What is (\partial)/(\partial y)(e^xsec^2(y)) ?
The answer to (\partial)/(\partial y)(e^xsec^2(y)) is 2e^xsec^2(y)tan(y)