What is the derivative of sec(xtan^2(x)) ?

The derivative of sec(xtan^2(x)) is tan^3(x)sec(x)+2sec^3(x)tan(x)

What is the first derivative of sec(xtan^2(x)) ?

The first derivative of sec(xtan^2(x)) is tan^3(x)sec(x)+2sec^3(x)tan(x)

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

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

Solution steps

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

Apply the Product Rule:

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

f = sec (x), g = tan^{2} (x)

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{x ^{2} - y}{x ^{2} + y})

\int \frac{8 cosh ( x )}{x} d x

\int \frac{( 5 - x )}{2 x ^{2} + x - 1} d x

x \to 0 lim (\frac{( 4 ^{2 x} - 1 )}{( 4 ^{x} - 1 )})

z \to 2 lim (\frac{z ^{2} + 3}{i z})

What is the derivative of sec(xtan^2(x)) ?
The derivative of sec(xtan^2(x)) is tan^3(x)sec(x)+2sec^3(x)tan(x)
What is the first derivative of sec(xtan^2(x)) ?
The first derivative of sec(xtan^2(x)) is tan^3(x)sec(x)+2sec^3(x)tan(x)