What is the derivative of (-7sin(x)/(4cos(x))) ?

The derivative of (-7sin(x)/(4cos(x))) is -7/4 sec^2(x)

What is the first derivative of (-7sin(x)/(4cos(x))) ?

The first derivative of (-7sin(x)/(4cos(x))) is -7/4 sec^2(x)

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\frac{d}{d x} (\frac{- 7 sin ( x )}{4 cos ( x )})

- \frac{7}{4} sec^{2} (x)

Solution steps

\frac{d}{d x} (\frac{- 7 sin ( x )}{4 cos ( x )})

Simplify

\frac{- 7 sin ( x )}{4 cos ( x )} : - \frac{7 tan ( x )}{4}

= \frac{d}{d x} (- \frac{7 tan ( x )}{4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{7}{4} \frac{d}{d x} (tan (x))

Apply the common derivative:

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

= - \frac{7}{4} sec^{2} (x)

What is the derivative of (-7sin(x)/(4cos(x))) ?
The derivative of (-7sin(x)/(4cos(x))) is -7/4 sec^2(x)
What is the first derivative of (-7sin(x)/(4cos(x))) ?
The first derivative of (-7sin(x)/(4cos(x))) is -7/4 sec^2(x)