What is the derivative of sin(xtan(x)) ?

The derivative of sin(xtan(x)) is sin(x)(1+sec^2(x))

What is the first derivative of sin(xtan(x)) ?

The first derivative of sin(xtan(x)) is sin(x)(1+sec^2(x))

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

sin (x) (1 + sec^{2} (x))

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = tan (x)

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

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

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

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

Simplify

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

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

((f (x))^{2})^{'}

\frac{d}{d x} (cos (2 x) e^{2 x})

x \to - 1 lim (\frac{2 x + 3}{x + 1})

(2 e^{x})^{^{'}}

What is the derivative of sin(xtan(x)) ?
The derivative of sin(xtan(x)) is sin(x)(1+sec^2(x))
What is the first derivative of sin(xtan(x)) ?
The first derivative of sin(xtan(x)) is sin(x)(1+sec^2(x))