What is the derivative of f(x)=(5^x)/(cos(x)) ?

The derivative of f(x)=(5^x)/(cos(x)) is 5^xln(5)sec(x)+sec(x)tan(x)*5^x

What is the first derivative of f(x)=(5^x)/(cos(x)) ?

The first derivative of f(x)=(5^x)/(cos(x)) is 5^xln(5)sec(x)+sec(x)tan(x)*5^x

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derivative of

f (x) = \frac{5 ^{x}}{cos ( x )}

5^{x} ln (5) sec (x) + sec (x) tan (x) \cdot 5^{x}

Solution steps

\frac{d}{d x} (\frac{5 ^{x}}{cos ( x )})

Simplify

\frac{5 ^{x}}{cos ( x )} : 5^{x} sec (x)

= \frac{d}{d x} (5^{x} sec (x))

Apply the Product Rule:

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

f = 5^{x}, g = sec (x)

= \frac{d}{d x} (5^{x}) sec (x) + \frac{d}{d x} (sec (x)) 5^{x}

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

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

= 5^{x} ln (5) sec (x) + sec (x) tan (x) \cdot 5^{x}

What is the derivative of f(x)=(5^x)/(cos(x)) ?
The derivative of f(x)=(5^x)/(cos(x)) is 5^xln(5)sec(x)+sec(x)tan(x)*5^x
What is the first derivative of f(x)=(5^x)/(cos(x)) ?
The first derivative of f(x)=(5^x)/(cos(x)) is 5^xln(5)sec(x)+sec(x)tan(x)*5^x