What is the derivative of 3e^{-x}*tan(3x) ?

The derivative of 3e^{-x}*tan(3x) is 3(-e^{-x}tan(3x)+3e^{-x}sec^2(3x))

What is the first derivative of 3e^{-x}*tan(3x) ?

The first derivative of 3e^{-x}*tan(3x) is 3(-e^{-x}tan(3x)+3e^{-x}sec^2(3x))

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\frac{d}{d x} (3 e^{- x} \cdot tan (3 x))

3 (- e^{- x} tan (3 x) + 3 e^{- x} sec^{2} (3 x))

Solution steps

\frac{d}{d x} (3 e^{- x} tan (3 x))

Take the constant out:

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

= 3 \frac{d}{d x} (e^{- x} tan (3 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x}, g = tan (3 x)

= 3 (\frac{d}{d x} (e^{- x}) tan (3 x) + \frac{d}{d x} (tan (3 x)) e^{- x})

\frac{d}{d x} (e^{- x}) = - e^{- x}

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

= 3 ((- e^{- x}) tan (3 x) + sec^{2} (3 x) \cdot 3 e^{- x})

Simplify

= 3 (- e^{- x} tan (3 x) + 3 e^{- x} sec^{2} (3 x))

\int (\frac{ln ( x )}{x ^{3}}) d x

\int_{0}^{1} \frac{x}{e ^{x}} d x

\frac{d x}{d t} = x^{2} + \frac{1}{49}

\frac{\partial}{\partial x} (ln (x y) + x e^{y})

3 z^{2} e^{z}

What is the derivative of 3e^{-x}*tan(3x) ?
The derivative of 3e^{-x}*tan(3x) is 3(-e^{-x}tan(3x)+3e^{-x}sec^2(3x))
What is the first derivative of 3e^{-x}*tan(3x) ?
The first derivative of 3e^{-x}*tan(3x) is 3(-e^{-x}tan(3x)+3e^{-x}sec^2(3x))