What is the derivative of tan(xsec^2(x)) ?

The derivative of tan(xsec^2(x)) is -2sec^2(x)+3sec^4(x)

What is the first derivative of tan(xsec^2(x)) ?

The first derivative of tan(xsec^2(x)) is -2sec^2(x)+3sec^4(x)

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

- 2 sec^{2} (x) + 3 sec^{4} (x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

sec^{2} (x) sec^{2} (x) + 2 sec^{2} (x) tan (x) tan (x) : - 2 sec^{2} (x) + 3 sec^{4} (x)

= - 2 sec^{2} (x) + 3 sec^{4} (x)

\int_{2}^{3} \frac{31}{3 - x} d x

(t sin (t))^{^{'}}

\frac{\partial}{\partial x} (e^{x z} y^{3} - ln (x))

\frac{d}{d x} (arctan (11 x))

e^{4 z} - 4 e^{- 4 z}

What is the derivative of tan(xsec^2(x)) ?
The derivative of tan(xsec^2(x)) is -2sec^2(x)+3sec^4(x)
What is the first derivative of tan(xsec^2(x)) ?
The first derivative of tan(xsec^2(x)) is -2sec^2(x)+3sec^4(x)