What is the derivative of ((1+tan(x)^2)/(sec(x))) ?

The derivative of ((1+tan(x)^2)/(sec(x))) is -sin(x)(1+tan(x))^2+2sec^2(x)cos(x)(1+tan(x))

What is the first derivative of ((1+tan(x)^2)/(sec(x))) ?

The first derivative of ((1+tan(x)^2)/(sec(x))) is -sin(x)(1+tan(x))^2+2sec^2(x)cos(x)(1+tan(x))

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

- sin (x) (1 + tan (x))^{2} + 2 sec^{2} (x) cos (x) (1 + tan (x))

Solution steps

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

Simplify

\frac{( 1 + tan ( x ) ) ^{2}}{sec ( x )} : cos (x) (1 + tan (x))^{2}

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

Apply the Product Rule:

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

f = cos (x), g = (1 + tan (x))^{2}

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

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

\frac{d}{d x} ((1 + tan (x))^{2}) = 2 (1 + tan (x)) sec^{2} (x)

= (- sin (x)) (1 + tan (x))^{2} + 2 (1 + tan (x)) sec^{2} (x) cos (x)

Simplify

= - sin (x) (1 + tan (x))^{2} + 2 sec^{2} (x) cos (x) (1 + tan (x))

(ln (\frac{x}{2}))^{^{'}}

y^{^{'}} = 5 x - y

\int 15 + \frac{200}{x + 1} d x

\frac{d}{d t} (sin (8 t))

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

What is the derivative of ((1+tan(x)^2)/(sec(x))) ?
The derivative of ((1+tan(x)^2)/(sec(x))) is -sin(x)(1+tan(x))^2+2sec^2(x)cos(x)(1+tan(x))
What is the first derivative of ((1+tan(x)^2)/(sec(x))) ?
The first derivative of ((1+tan(x)^2)/(sec(x))) is -sin(x)(1+tan(x))^2+2sec^2(x)cos(x)(1+tan(x))