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Popular >

derivative of (sin(x)/(x+1))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x + 1) = 1

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

Simplify

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

Popular Examples

limit as x approaches 0 of ((2x^2-3x))/x

x \to 0 lim (\frac{( 2 x ^{2} - 3 x )}{x})

laplacetransform 3*(5e^{-5.06s})+3*(2.26*5e^{-5.06s})laplace transform

3 \cdot (5 e^{- 5.06 s}) + 3 \cdot (2.26 \cdot 5 e^{- 5.06 s})

integral of ((9sqrt(4-x^2)))/2

\int \frac{( 9 4 - x ^{2} )}{2} d x

(\partial)/(\partial x)(sin(2x+y))

\frac{\partial}{\partial x} (sin (2 x + y))

derivative of-(x-3^2)

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

Frequently Asked Questions (FAQ)

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