What is the derivative of (5x^2tan(x))/(sec(x)) ?

The derivative of (5x^2tan(x))/(sec(x)) is 5(x^2cos(x)+2xsin(x))

What is the first derivative of (5x^2tan(x))/(sec(x)) ?

The first derivative of (5x^2tan(x))/(sec(x)) is 5(x^2cos(x)+2xsin(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{5 x ^{2} tan ( x )}{sec ( x )}

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

Solution steps

\frac{d}{d x} (\frac{5 x ^{2} tan ( x )}{sec ( x )})

Simplify

\frac{5 x ^{2} tan ( x )}{sec ( x )} : 5 x^{2} tan (x) cos (x)

= \frac{d}{d x} (5 x^{2} tan (x) cos (x))

Take the constant out:

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

= 5 \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)

= 5 (\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)

= 5 (2 x tan (x) cos (x) + cos (x) x^{2})

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

= 5 (x^{2} cos (x) + 2 x sin (x))

\int \frac{x ^{2}}{x - 9} d x

2 - x^{2}, x^{2}

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 9 x z - 12)

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

What is the derivative of (5x^2tan(x))/(sec(x)) ?
The derivative of (5x^2tan(x))/(sec(x)) is 5(x^2cos(x)+2xsin(x))
What is the first derivative of (5x^2tan(x))/(sec(x)) ?
The first derivative of (5x^2tan(x))/(sec(x)) is 5(x^2cos(x)+2xsin(x))