What is the derivative of (sin(x+cos(x))/(cos(x))) ?

The derivative of (sin(x+cos(x))/(cos(x))) is sec^2(x)

What is the first derivative of (sin(x+cos(x))/(cos(x))) ?

The first derivative of (sin(x+cos(x))/(cos(x))) is sec^2(x)

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\frac{d}{d x} (\frac{sin ( x ) + cos ( x )}{cos ( x )})

sec^{2} (x)

Solution steps

\frac{d}{d x} (\frac{sin ( x ) + cos ( x )}{cos ( x )})

Simplify

\frac{sin ( x ) + cos ( x )}{cos ( x )} : 1 + tan (x)

= \frac{d}{d x} (1 + tan (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) + \frac{d}{d x} (tan (x))

\frac{d}{d x} (1) = 0

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

= 0 + sec^{2} (x)

Simplify

= sec^{2} (x)

\frac{\partial}{\partial x} (sin (y^{2}) + 6 e^{x})

e^{2 y}

(\frac{( s + 1 )}{s ^{4}})^{3}

\int x (x + 1)^{5} d x

\int (3 x - 4) e^{(- x)} d x

What is the derivative of (sin(x+cos(x))/(cos(x))) ?
The derivative of (sin(x+cos(x))/(cos(x))) is sec^2(x)
What is the first derivative of (sin(x+cos(x))/(cos(x))) ?
The first derivative of (sin(x+cos(x))/(cos(x))) is sec^2(x)