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

The derivative of (sec^2(x)dx) is d(2xsec^2(x)tan(x)+sec^2(x))

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

The first derivative of (sec^2(x)dx) is d(2xsec^2(x)tan(x)+sec^2(x))

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

f (t) = t^{6} sin (t)

cos (- x)

\frac{\partial}{\partial y} (5 x + 4 y)

\int 2 x e^{3 x^{2}} d x

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

What is the derivative of (sec^2(x)dx) ?
The derivative of (sec^2(x)dx) is d(2xsec^2(x)tan(x)+sec^2(x))
What is the first derivative of (sec^2(x)dx) ?
The first derivative of (sec^2(x)dx) is d(2xsec^2(x)tan(x)+sec^2(x))