What is the derivative of (sin(x)-1)/(sin(x)+4) ?

The derivative of (sin(x)-1)/(sin(x)+4) is (5cos(x))/((sin(x)+4)^2)

What is the first derivative of (sin(x)-1)/(sin(x)+4) ?

The first derivative of (sin(x)-1)/(sin(x)+4) is (5cos(x))/((sin(x)+4)^2)

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derivative of

\frac{sin ( x ) - 1}{sin ( x ) + 4}

\frac{5 cos ( x )}{( sin ( x ) + 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{sin ( x ) - 1}{sin ( x ) + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( sin ( x ) - 1 ) ( sin ( x ) + 4 ) - \frac{d}{d x} ( sin ( x ) + 4 ) ( sin ( x ) - 1 )}{( sin ( x ) + 4 ) ^{2}}

\frac{d}{d x} (sin (x) - 1) = cos (x)

\frac{d}{d x} (sin (x) + 4) = cos (x)

= \frac{cos ( x ) ( sin ( x ) + 4 ) - cos ( x ) ( sin ( x ) - 1 )}{( sin ( x ) + 4 ) ^{2}}

Expand

cos (x) (sin (x) + 4) - cos (x) (sin (x) - 1) : 5 cos (x)

= \frac{5 cos ( x )}{( sin ( x ) + 4 ) ^{2}}

\int \frac{1}{f ( x )} d x

\int 1 - cos (2 t) d t

y = x^{3} - 2 x - 2, at x = 1

- sin (x)

\frac{d}{d x} (x^{p} e^{a x})

What is the derivative of (sin(x)-1)/(sin(x)+4) ?
The derivative of (sin(x)-1)/(sin(x)+4) is (5cos(x))/((sin(x)+4)^2)
What is the first derivative of (sin(x)-1)/(sin(x)+4) ?
The first derivative of (sin(x)-1)/(sin(x)+4) is (5cos(x))/((sin(x)+4)^2)