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Popular >

derivative of (sin(x)+cos(x))/(cos(x))

Solution

derivative of

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

Solution

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)

Popular Examples

tangent of y=(8x)/(x^2+1),(-1,-4)tangent of

y = \frac{8 x}{x ^{2} + 1}, (- 1, - 4)

integral of 1/(sqrt(x^2+2x-24))

\int \frac{1}{x ^{2} + 2 x - 24} d x

(\partial)/(\partial y)(((x^2y))/(x^2+y^2))

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

slope of 6x^2+2xy+2y^2=74,(3,2)slope

6 x^{2} + 2 x y + 2 y^{2} = 74, (3, 2)

f(t)=\sqrt[3]{t}

Frequently Asked Questions (FAQ)

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)