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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 \cdot 2 sec (2 x + 3 y) sec (2 x + 3 y) tan (2 x + 3 y) \cdot 2 : 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 \frac{e ^{x}}{4 - e ^{x}} d x

x \to 0 lim (\frac{sin ( x ) - 2 x}{x})

\frac{d}{d x} (\frac{x}{x - 1})

\int \frac{4 x ^{2}}{x ^{2}} d x

\int \frac{2 x ^{2} + 9 x + 2}{( x ^{2} + 1 ) ^{2}} d x

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