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

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

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

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

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\frac{d}{d 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}

x \to 5 lim (3 x - 7)

y = x^{4} - 4 x^{2}, y = x^{2} - 4

y^{^{'}} = \frac{x ^{4}}{16} (e^{- y})

\int \frac{2}{3 x - 4} d x

\frac{d}{d x} (x (1 - x)^{3})

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