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Popular >

derivative of (1-sin(x)/(cos(x)))

Solution

\frac{d}{d x} (\frac{1 - sin ( x )}{cos ( x )})

Solution

sec (x) tan (x) - sec^{2} (x)

Solution steps

\frac{d}{d x} (\frac{1 - sin ( x )}{cos ( x )})

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= sec (x) tan (x) - sec^{2} (x)

Graph

Popular Examples

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f (x) = \frac{1 + 2 x}{1 - 2 x}, (1, - 3)

area y=|2x-6|,y=x area

y = ∣ 2 x - 6 ∣, y = x

derivative of 6x^2+4x

\frac{d}{d x} (6 x^{2} + 4 x)

derivative of f(x)=(66)/((1-x)^4)derivative of

f (x) = \frac{66}{( 1 - x ) ^{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of (1-sin(x)/(cos(x))) ?
The derivative of (1-sin(x)/(cos(x))) is sec(x)tan(x)-sec^2(x)
What is the first derivative of (1-sin(x)/(cos(x))) ?
The first derivative of (1-sin(x)/(cos(x))) is sec(x)tan(x)-sec^2(x)