What is the derivative of (sin(q)+cos(q))/(cos(q)) ?

The derivative of (sin(q)+cos(q))/(cos(q)) is sec^2(q)

What is the first derivative of (sin(q)+cos(q))/(cos(q)) ?

The first derivative of (sin(q)+cos(q))/(cos(q)) is sec^2(q)

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derivative of

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

sec^{2} (q)

Solution steps

\frac{d}{d q} (\frac{sin ( q ) + cos ( q )}{cos ( q )})

Simplify

\frac{sin ( q ) + cos ( q )}{cos ( q )} : 1 + tan (q)

= \frac{d}{d q} (1 + tan (q))

Apply the Sum/Difference Rule:

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

= \frac{d}{d q} (1) + \frac{d}{d q} (tan (q))

\frac{d}{d q} (1) = 0

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

= 0 + sec^{2} (q)

Simplify

= sec^{2} (q)

y^{^{''}} - 10 y^{^{'}} + 21 y = 0

\frac{4}{s ( s ^{2} + 2 s + 4 )}

x \to - 8 lim (3 x + 1)

\frac{d}{d x} (cos^{2} (x) + 1)

x \to 5 lim (\frac{x + 2}{x ^{2} - 5})

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