What is the derivative of tan(xy) ?

The derivative of tan(xy) is sec^2(xy)(y+x(dy)/(dx))

What is the first derivative of tan(xy) ?

The first derivative of tan(xy) is sec^2(xy)(y+x(dy)/(dx))

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\frac{d}{d x} (tan (x y))

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

Solution steps

\frac{d}{d x} (tan (x y))

Apply the chain rule:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

What is the derivative of tan(xy) ?
The derivative of tan(xy) is sec^2(xy)(y+x(dy)/(dx))
What is the first derivative of tan(xy) ?
The first derivative of tan(xy) is sec^2(xy)(y+x(dy)/(dx))