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

The answer to (\partial)/(\partial x)(sec^2(xy^2)y^2) is 2y^4sec^2(xy^2)tan(xy^2)

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(\partial)/(\partial x)(sec^2(xy^2)y^2)

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

2 y^{4} sec^{2} (x y^{2}) tan (x y^{2})

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

y^{2} \cdot 2 sec (x y^{2}) sec (x y^{2}) tan (x y^{2}) y^{2} : 2 y^{4} sec^{2} (x y^{2}) tan (x y^{2})

= 2 y^{4} sec^{2} (x y^{2}) tan (x y^{2})

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What is (\partial)/(\partial x)(sec^2(xy^2)y^2) ?
The answer to (\partial)/(\partial x)(sec^2(xy^2)y^2) is 2y^4sec^2(xy^2)tan(xy^2)