What is the derivative of 5tan(3x) ?

The derivative of 5tan(3x) is 15sec^2(3x)

What is the first derivative of 5tan(3x) ?

The first derivative of 5tan(3x) is 15sec^2(3x)

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\frac{d}{d x} (5 tan (3 x))

15 sec^{2} (3 x)

Solution steps

\frac{d}{d x} (5 tan (3 x))

Take the constant out:

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

= 5 \frac{d}{d x} (tan (3 x))

Apply the chain rule:

sec^{2} (3 x) \frac{d}{d x} (3 x)

= sec^{2} (3 x) \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= 5 sec^{2} (3 x) \cdot 3

Simplify

= 15 sec^{2} (3 x)

What is the derivative of 5tan(3x) ?
The derivative of 5tan(3x) is 15sec^2(3x)
What is the first derivative of 5tan(3x) ?
The first derivative of 5tan(3x) is 15sec^2(3x)