What is the derivative of (sin(x)/(cos^2(x))) ?

The derivative of (sin(x)/(cos^2(x))) is -sec(x)+2sec^3(x)

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

The first derivative of (sin(x)/(cos^2(x))) is -sec(x)+2sec^3(x)

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\frac{d}{d x} (\frac{sin ( x )}{cos ^{2} ( x )})

- sec (x) + 2 sec^{3} (x)

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{cos ^{2} ( x )})

Simplify

\frac{sin ( x )}{cos ^{2} ( x )} : sec (x) tan (x)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (x), g = tan (x)

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

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

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

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

Simplify

sec (x) tan (x) tan (x) + sec^{2} (x) sec (x) : - sec (x) + 2 sec^{3} (x)

= - sec (x) + 2 sec^{3} (x)

\frac{d}{d x} (4 - x^{\frac{2}{3}})

\frac{d}{d x} (x^{\frac{4}{3}} - 5)

\int_{- 1}^{3} (1 + 4 x) d x

f (x) = arctan (cos (x))

\frac{d}{d x} (3 x^{3} + 5 x)

What is the derivative of (sin(x)/(cos^2(x))) ?
The derivative of (sin(x)/(cos^2(x))) is -sec(x)+2sec^3(x)
What is the first derivative of (sin(x)/(cos^2(x))) ?
The first derivative of (sin(x)/(cos^2(x))) is -sec(x)+2sec^3(x)