What is the derivative of (sin(x)/(bsin(bx))) ?

The derivative of (sin(x)/(bsin(bx))) is (sin(bx)cos(x)-bcos(bx)sin(x))/(bsin^2(bx))

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

The first derivative of (sin(x)/(bsin(bx))) is (sin(bx)cos(x)-bcos(bx)sin(x))/(bsin^2(bx))

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

\frac{sin ( b x ) cos ( x ) - b cos ( b x ) sin ( x )}{b sin ^{2} ( b x )}

Solution steps

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

Take the constant out:

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

= \frac{1}{b} \frac{d}{d x} (\frac{sin ( x )}{sin ( b x )})

Apply the Quotient Rule:

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

= \frac{1}{b} \cdot \frac{\frac{d}{d x} ( sin ( x ) ) sin ( b x ) - \frac{d}{d x} ( sin ( b x ) ) sin ( x )}{( sin ( b x ) ) ^{2}}

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

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

= \frac{1}{b} \cdot \frac{cos ( x ) sin ( b x ) - cos ( b x ) b sin ( x )}{( sin ( b x ) ) ^{2}}

Simplify

\frac{1}{b} \cdot \frac{cos ( x ) sin ( b x ) - cos ( b x ) b sin ( x )}{sin ^{2} ( b x )} : \frac{sin ( b x ) cos ( x ) - b cos ( b x ) sin ( x )}{b sin ^{2} ( b x )}

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

y^{^{'}} - 2 x y = 2 x e^{x^{2}}

((4 x^{2} + 5)^{2} \cdot (7 x)^{2 x})^{^{'}}

- 4 x^{2} y + y^{^{'}} = 4 x^{2}

\int \frac{1}{12 x + 12 x} d x

\int x \cdot (7 - x)^{9} d x

What is the derivative of (sin(x)/(bsin(bx))) ?
The derivative of (sin(x)/(bsin(bx))) is (sin(bx)cos(x)-bcos(bx)sin(x))/(bsin^2(bx))
What is the first derivative of (sin(x)/(bsin(bx))) ?
The first derivative of (sin(x)/(bsin(bx))) is (sin(bx)cos(x)-bcos(bx)sin(x))/(bsin^2(bx))