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

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

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

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

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\frac{d}{d 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))

\frac{d}{d x} (ln (10 - x))

\int sec^{2} (θ) tan^{3} (θ) d θ

\int \frac{( x + 2 )}{x} d x

x \to 0 lim (x^{2} ln ∣ x ∣)

\frac{\partial}{\partial x} (y^{x^{y}})

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