What is the derivative of f(x)=(sin(pi-x))/(pi-x) ?

The derivative of f(x)=(sin(pi-x))/(pi-x) is (-cos(pi-x)(pi-x)+sin(pi-x))/((pi-x)^2)

What is the first derivative of f(x)=(sin(pi-x))/(pi-x) ?

The first derivative of f(x)=(sin(pi-x))/(pi-x) is (-cos(pi-x)(pi-x)+sin(pi-x))/((pi-x)^2)

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derivative of

f (x) = \frac{sin ( π - x )}{π - x}

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

Solution steps

\frac{d}{d x} (\frac{sin ( π - x )}{π - x})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (π - x) = - 1

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

Simplify

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

x \to 0 lim (5^{x + h} - 5^{x})

y^{^{'}} - tan (x) = 0

x - y

\int x cos (1 - x^{2}) d x

y = x^{12}

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