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

The answer to (\partial)/(\partial y)(sec^2(yt)) is 2tsec^2(yt)tan(yt)

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

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

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

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

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

= 2 sec (y t) sec (y t) tan (y t) t

Simplify

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

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

\frac{d}{d x} (e^{2 s i n (3 x)})

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f (x) = \frac{sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )}

\int (2 x - 4)^{2} d x

y^{^{''}} + 4 y = x - \frac{1}{20} x^{2}

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