What is the derivative of (sin(x)/(xy)) ?

The derivative of (sin(x)/(xy)) is (xcos(x)y-sin(x)(y+x\frac{dy)/(dx))}{x^2y^2}

What is the first derivative of (sin(x)/(xy)) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

\int 2 x^{2} + 3 x - 1 d x

f (x) = \frac{x}{x ^{2} + 5}

\int_{0}^{3} x^{2} e^{- x} d x

x^{\frac{5}{2}}

\int (lo g_{e} (x))^{2} d x

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