What is the derivative of tan(ax) ?

The derivative of tan(ax) is sec^2(ax)a

What is the first derivative of tan(ax) ?

The first derivative of tan(ax) is sec^2(ax)a

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

sec^{2} (a x) a

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (a x) = a

= sec^{2} (a x) a

What is the derivative of tan(ax) ?
The derivative of tan(ax) is sec^2(ax)a
What is the first derivative of tan(ax) ?
The first derivative of tan(ax) is sec^2(ax)a