What is (\partial)/(\partial y)(ytsec^2(yt)) ?

The answer to (\partial)/(\partial y)(ytsec^2(yt)) is t(sec^2(yt)+2ytsec^2(yt)tan(yt))

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(\partial)/(\partial y)(ytsec^2(yt))

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

t (sec^{2} (y t) + 2 y t sec^{2} (y t) tan (y t))

Solution steps

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

Treat

t

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = sec^{2} (y t)

= t (\frac{\partial}{\partial y} (y) sec^{2} (y t) + \frac{\partial}{\partial y} (sec^{2} (y t)) y)

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (sec^{2} (y t)) = 2 t sec^{2} (t y) tan (t y)

= t (1 \cdot sec^{2} (y t) + 2 t sec^{2} (t y) tan (t y) y)

Simplify

= t (sec^{2} (y t) + 2 y t sec^{2} (y t) tan (y t))

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What is (\partial)/(\partial y)(ytsec^2(yt)) ?
The answer to (\partial)/(\partial y)(ytsec^2(yt)) is t(sec^2(yt)+2ytsec^2(yt)tan(yt))