What is the derivative of 12tan(cosh(e^{4x})) ?

The derivative of 12tan(cosh(e^{4x})) is 48e^{4x}sec^2(cosh(e^{4x}))sinh(e^{4x})

What is the first derivative of 12tan(cosh(e^{4x})) ?

The first derivative of 12tan(cosh(e^{4x})) is 48e^{4x}sec^2(cosh(e^{4x}))sinh(e^{4x})

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\frac{d}{d x} (12 tan (cosh (e^{4 x})))

48 e^{4 x} sec^{2} (cosh (e^{4 x})) sinh (e^{4 x})

Solution steps

\frac{d}{d x} (12 tan (cosh (e^{4 x})))

Take the constant out:

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

= 12 \frac{d}{d x} (tan (cosh (e^{4 x})))

Apply the chain rule:

sec^{2} (cosh (e^{4 x})) \frac{d}{d x} (cosh (e^{4 x}))

= sec^{2} (cosh (e^{4 x})) \frac{d}{d x} (cosh (e^{4 x}))

\frac{d}{d x} (cosh (e^{4 x})) = sinh (e^{4 x}) e^{4 x} \cdot 4

= 12 sec^{2} (cosh (e^{4 x})) sinh (e^{4 x}) e^{4 x} \cdot 4

Simplify

= 48 e^{4 x} sec^{2} (cosh (e^{4 x})) sinh (e^{4 x})

\int (e^{- x} - e^{3}) (e^{x} - e^{- 5}) d x

y = e^{7 t s i n (2 t)}

\int (x^{\frac{3}{2}} + 4 x + 6) d x

\int \frac{1}{4} e^{- \frac{x}{4}} d x

y = f (x), at x = 2

What is the derivative of 12tan(cosh(e^{4x})) ?
The derivative of 12tan(cosh(e^{4x})) is 48e^{4x}sec^2(cosh(e^{4x}))sinh(e^{4x})
What is the first derivative of 12tan(cosh(e^{4x})) ?
The first derivative of 12tan(cosh(e^{4x})) is 48e^{4x}sec^2(cosh(e^{4x}))sinh(e^{4x})