What is the derivative of (4sin(x))/(6-7sin(x)) ?

The derivative of (4sin(x))/(6-7sin(x)) is (24cos(x))/((6-7sin(x))^2)

What is the first derivative of (4sin(x))/(6-7sin(x)) ?

The first derivative of (4sin(x))/(6-7sin(x)) is (24cos(x))/((6-7sin(x))^2)

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derivative of

\frac{4 sin ( x )}{6 - 7 sin ( x )}

\frac{24 cos ( x )}{( 6 - 7 sin ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 sin ( x )}{6 - 7 sin ( x )})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{sin ( x )}{6 - 7 sin ( x )})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d}{d x} ( sin ( x ) ) ( 6 - 7 sin ( x ) ) - \frac{d}{d x} ( 6 - 7 sin ( x ) ) sin ( x )}{( 6 - 7 sin ( x ) ) ^{2}}

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

\frac{d}{d x} (6 - 7 sin (x)) = - 7 cos (x)

= 4 \cdot \frac{cos ( x ) ( 6 - 7 sin ( x ) ) - ( - 7 cos ( x ) ) sin ( x )}{( 6 - 7 sin ( x ) ) ^{2}}

Simplify

4 \cdot \frac{cos ( x ) ( 6 - 7 sin ( x ) ) - ( - 7 cos ( x ) ) sin ( x )}{( 6 - 7 sin ( x ) ) ^{2}} : \frac{24 cos ( x )}{( 6 - 7 sin ( x ) ) ^{2}}

= \frac{24 cos ( x )}{( 6 - 7 sin ( x ) ) ^{2}}

\frac{\partial}{\partial x} (e^{- x} cos (- 8 y))

f (x) = \frac{12}{ln ( x )}

\frac{1}{( s ^{2} + 3 s + 2 )}

x \to \infty lim (cos (x))

\int_{- 2}^{3} \frac{20}{x ^{4}} d x

What is the derivative of (4sin(x))/(6-7sin(x)) ?
The derivative of (4sin(x))/(6-7sin(x)) is (24cos(x))/((6-7sin(x))^2)
What is the first derivative of (4sin(x))/(6-7sin(x)) ?
The first derivative of (4sin(x))/(6-7sin(x)) is (24cos(x))/((6-7sin(x))^2)