What is the derivative of ((7-5x)/(cos(x))) ?

The derivative of ((7-5x)/(cos(x))) is (-5cos(x)+sin(x)(7-5x))/(cos^2(x))

What is the first derivative of ((7-5x)/(cos(x))) ?

The first derivative of ((7-5x)/(cos(x))) is (-5cos(x)+sin(x)(7-5x))/(cos^2(x))

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\frac{d}{d x} (\frac{( 7 - 5 x )}{cos ( x )})

\frac{- 5 cos ( x ) + sin ( x ) ( 7 - 5 x )}{cos ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{( 7 - 5 x )}{cos ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 - 5 x ) cos ( x ) - \frac{d}{d x} ( cos ( x ) ) ( 7 - 5 x )}{( cos ( x ) ) ^{2}}

\frac{d}{d x} (7 - 5 x) = - 5

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

= \frac{( - 5 ) cos ( x ) - ( - sin ( x ) ) ( 7 - 5 x )}{( cos ( x ) ) ^{2}}

Simplify

= \frac{- 5 cos ( x ) + sin ( x ) ( 7 - 5 x )}{cos ^{2} ( x )}

\int (100 - x)^{2} d x

y = e^{- x^{2}}

f (x) = \frac{x ^{2} + 1}{x}

\frac{\partial}{\partial y} (x e^{y} + y + 1)

\frac{d}{d t} (\frac{6 t + 28}{t + 7})

What is the derivative of ((7-5x)/(cos(x))) ?
The derivative of ((7-5x)/(cos(x))) is (-5cos(x)+sin(x)(7-5x))/(cos^2(x))
What is the first derivative of ((7-5x)/(cos(x))) ?
The first derivative of ((7-5x)/(cos(x))) is (-5cos(x)+sin(x)(7-5x))/(cos^2(x))