en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2tan(xy)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

derivative of (3x+1/(7x+5))

\frac{d}{d x} (\frac{3 x + 1}{7 x + 5})

derivative of (x^x/(sin(x)))

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

roots asin(t/c)roots

a sin (\frac{t}{c})

integral of x^{1/3}sin(x^{4/3}+8)

\int x^{\frac{1}{3}} sin (x^{\frac{4}{3}} + 8) d x

limit as x approaches 0+of 1/x-1/(e^x-1)

x \to 0 + lim (\frac{1}{x} - \frac{1}{e ^{x} - 1})

Frequently Asked Questions (FAQ)

What is the derivative of x^2tan(xy) ?
The derivative of x^2tan(xy) is 2xtan(xy)+sec^2(xy)(y+x(dy)/(dx))x^2
What is the first derivative of x^2tan(xy) ?
The first derivative of x^2tan(xy) is 2xtan(xy)+sec^2(xy)(y+x(dy)/(dx))x^2