What is the derivative of (0.6e^x/(cos(x))) ?

The derivative of (0.6e^x/(cos(x))) is 0.6sec(x)(e^x+e^xtan(x))

What is the first derivative of (0.6e^x/(cos(x))) ?

The first derivative of (0.6e^x/(cos(x))) is 0.6sec(x)(e^x+e^xtan(x))

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\frac{d}{d x} (\frac{0.6 e ^{x}}{cos ( x )})

0.6 sec (x) (e^{x} + e^{x} tan (x))

Solution steps

\frac{d}{d x} (\frac{0.6 e ^{x}}{cos ( x )})

Simplify

\frac{0.6 e ^{x}}{cos ( x )} : 0.6 e^{x} sec (x)

= \frac{d}{d x} (0.6 e^{x} sec (x))

Take the constant out:

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

= 0.6 \frac{d}{d x} (e^{x} sec (x))

Apply the Product Rule:

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

f = e^{x}, g = sec (x)

= 0.6 (\frac{d}{d x} (e^{x}) sec (x) + \frac{d}{d x} (sec (x)) e^{x})

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= 0.6 (e^{x} sec (x) + sec (x) tan (x) e^{x})

Simplify

0.6 (e^{x} sec (x) + sec (x) tan (x) e^{x}) : 0.6 sec (x) (e^{x} + e^{x} tan (x))

= 0.6 sec (x) (e^{x} + e^{x} tan (x))

x + 3

\int \frac{7}{( 7 ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (\frac{5}{x + 2})

x \to 0 lim (x [\frac{1}{x}])

\frac{d}{d s} (\frac{1}{s})

What is the derivative of (0.6e^x/(cos(x))) ?
The derivative of (0.6e^x/(cos(x))) is 0.6sec(x)(e^x+e^xtan(x))
What is the first derivative of (0.6e^x/(cos(x))) ?
The first derivative of (0.6e^x/(cos(x))) is 0.6sec(x)(e^x+e^xtan(x))