Find the derivative of sec(xy)

 Exercise

$\frac{dy}{dx}\sec\left(xy\right)$

 

Taking the derivative of secant function: $\frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x)$

$\frac{d}{dx}\left(xy\right)\sec\left(xy\right)\tan\left(xy\right)$

 

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$y\frac{d}{dx}\left(x\right)\sec\left(xy\right)\tan\left(xy\right)$

 

The derivative of the linear function is equal to $1$

$y\sec\left(xy\right)\tan\left(xy\right)$

$y\sec\left(xy\right)\tan\left(xy\right)$

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