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Popular >

derivative of (x+4/(cos(x)))

Solution

\frac{d}{d x} (\frac{x + 4}{cos ( x )})

Solution

\frac{cos ( x ) + sin ( x ) ( x + 4 )}{cos ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{x + 4}{cos ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x + 4 ) cos ( x ) - \frac{d}{d x} ( cos ( x ) ) ( x + 4 )}{( cos ( x ) ) ^{2}}

\frac{d}{d x} (x + 4) = 1

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

= \frac{1 \cdot cos ( x ) - ( - sin ( x ) ) ( x + 4 )}{( cos ( x ) ) ^{2}}

Simplify

= \frac{cos ( x ) + sin ( x ) ( x + 4 )}{cos ^{2} ( x )}

Popular Examples

(\partial)/(\partial x)(xe^{y^2}+yln(x))

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

derivative of f(x)=(2x-3)*sqrt(x)derivative of

f (x) = (2 x - 3) \cdot x

integral of 1-2/(x^2)

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

integral of (e^x)/(sqrt(e^x+1)+1)

\int \frac{e ^{x}}{e ^{x} + 1 + 1} d x

integral of ((2x+3)^2)/(sqrt(x))

\int \frac{( 2 x + 3 ) ^{2}}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+4/(cos(x))) ?
The derivative of (x+4/(cos(x))) is (cos(x)+sin(x)(x+4))/(cos^2(x))
What is the first derivative of (x+4/(cos(x))) ?
The first derivative of (x+4/(cos(x))) is (cos(x)+sin(x)(x+4))/(cos^2(x))