What is the derivative of (tan(x)dx) ?

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

What is the first derivative of (tan(x)dx) ?

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

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

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

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = tan (x), g = x

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

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

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

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

Simplify

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

\frac{d y}{d x} - 2 y + x^{2} = 0

\int_{1}^{11} \frac{1}{x - 7} d x

\frac{d}{d x} ((x + 5 x) (x^{\frac{3}{2}} - x))

f (x) = 3 x^{4} - 12 x^{3} + 4

(1 + x^{2})^{\frac{1}{2}}

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