What is the derivative of f(x)=(2x^2tan(x))/(sec(x)) ?

The derivative of f(x)=(2x^2tan(x))/(sec(x)) is 2(x^2cos(x)+2xsin(x))

What is the first derivative of f(x)=(2x^2tan(x))/(sec(x)) ?

The first derivative of f(x)=(2x^2tan(x))/(sec(x)) is 2(x^2cos(x)+2xsin(x))

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derivative of

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

2 (x^{2} cos (x) + 2 x sin (x))

Solution steps

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

Simplify

\frac{2 x ^{2} tan ( x )}{sec ( x )} : 2 x^{2} tan (x) cos (x)

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

cos (x) tan (x) = sin (x)

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

What is the derivative of f(x)=(2x^2tan(x))/(sec(x)) ?
The derivative of f(x)=(2x^2tan(x))/(sec(x)) is 2(x^2cos(x)+2xsin(x))
What is the first derivative of f(x)=(2x^2tan(x))/(sec(x)) ?
The first derivative of f(x)=(2x^2tan(x))/(sec(x)) is 2(x^2cos(x)+2xsin(x))