What is (\partial)/(\partial y)(2sec^2(2x+3y)) ?

The answer to (\partial)/(\partial y)(2sec^2(2x+3y)) is 12sec^2(2x+3y)tan(2x+3y)

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(\partial)/(\partial y)(2sec^2(2x+3y))

\frac{\partial}{\partial y} (2 sec^{2} (2 x + 3 y))

12 sec^{2} (2 x + 3 y) tan (2 x + 3 y)

Solution steps

\frac{\partial}{\partial y} (2 sec^{2} (2 x + 3 y))

Treat

x

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial y} (sec^{2} (2 x + 3 y))

Apply the chain rule:

2 sec (2 x + 3 y) \frac{\partial}{\partial y} (sec (2 x + 3 y))

= 2 sec (2 x + 3 y) \frac{\partial}{\partial y} (sec (2 x + 3 y))

\frac{\partial}{\partial y} (sec (2 x + 3 y)) = sec (2 x + 3 y) tan (2 x + 3 y) \cdot 3

= 2 \cdot 2 sec (2 x + 3 y) sec (2 x + 3 y) tan (2 x + 3 y) \cdot 3

Simplify

2 \cdot 2 sec (2 x + 3 y) sec (2 x + 3 y) tan (2 x + 3 y) \cdot 3 : 12 sec^{2} (2 x + 3 y) tan (2 x + 3 y)

= 12 sec^{2} (2 x + 3 y) tan (2 x + 3 y)

\int 4 - 9 x^{2} d x

e^{x - y}

y = 7

\int x^{2} (x^{3} + 1)^{\frac{1}{2}} d x

c^{\frac{1}{2}}

What is (\partial)/(\partial y)(2sec^2(2x+3y)) ?
The answer to (\partial)/(\partial y)(2sec^2(2x+3y)) is 12sec^2(2x+3y)tan(2x+3y)