What is the derivative of (sin(x)/(y^2)) ?

The derivative of (sin(x)/(y^2)) is (cos(x)y-2sin(x)\frac{dy)/(dx)}{y^3}

What is the first derivative of (sin(x)/(y^2)) ?

The first derivative of (sin(x)/(y^2)) is (cos(x)y-2sin(x)\frac{dy)/(dx)}{y^3}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{cos ( x ) y - 2 sin ( x ) \frac{d y}{d x}}{y ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( x ) ) y ^{2} - \frac{d}{d x} ( y ^{2} ) sin ( x )}{( y ^{2} ) ^{2}}

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

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

= \frac{cos ( x ) y ^{2} - 2 y \frac{d y}{d x} sin ( x )}{( y ^{2} ) ^{2}}

Simplify

\frac{cos ( x ) y ^{2} - 2 y \frac{d y}{d x} sin ( x )}{( y ^{2} ) ^{2}} : \frac{cos ( x ) y - 2 sin ( x ) \frac{d y}{d x}}{y ^{3}}

= \frac{cos ( x ) y - 2 sin ( x ) \frac{d y}{d x}}{y ^{3}}

\frac{d}{d x} (3 \cdot ln (x))

\frac{d}{d x} (- 7 x)

(1 + e^{2 t})^{2}

2 y^{^{''}} + 12 y^{^{'}} + 50 y = 0

\int cos^{2} (2 x) sin (2 x) d x

What is the derivative of (sin(x)/(y^2)) ?
The derivative of (sin(x)/(y^2)) is (cos(x)y-2sin(x)\frac{dy)/(dx)}{y^3}
What is the first derivative of (sin(x)/(y^2)) ?
The first derivative of (sin(x)/(y^2)) is (cos(x)y-2sin(x)\frac{dy)/(dx)}{y^3}