What is the derivative of tan(Inx) ?

The derivative of tan(Inx) is sec^2(Inx)In

What is the first derivative of tan(Inx) ?

The first derivative of tan(Inx) is sec^2(Inx)In

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\frac{d}{d x} (tan (I n x))

sec^{2} (I n x) I n

Solution steps

\frac{d}{d x} (tan (I n x))

Treat

n, I

as a constant

Apply the chain rule:

sec^{2} (I n x) \frac{d}{d x} (I n x)

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

\frac{d}{d x} (I n x) = I n

= sec^{2} (I n x) I n

What is the derivative of tan(Inx) ?
The derivative of tan(Inx) is sec^2(Inx)In
What is the first derivative of tan(Inx) ?
The first derivative of tan(Inx) is sec^2(Inx)In