What is the derivative of (e^{sin(x})/(2+cos(pi)x)) ?

The derivative of (e^{sin(x})/(2+cos(pi)x)) is (e^{sin(x)}cos(x)(2-x)+e^{sin(x)})/((2-x)^2)

What is the first derivative of (e^{sin(x})/(2+cos(pi)x)) ?

The first derivative of (e^{sin(x})/(2+cos(pi)x)) is (e^{sin(x)}cos(x)(2-x)+e^{sin(x)})/((2-x)^2)

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\frac{d}{d x} (\frac{e ^{s i n (x)}}{2 + cos ( π ) x})

\frac{e ^{s i n (x)} cos ( x ) ( 2 - x ) + e ^{s i n (x)}}{( 2 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{s i n (x)}}{2 + cos ( π ) x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{s i n (x)} ) ( 2 + cos ( π ) x ) - \frac{d}{d x} ( 2 + cos ( π ) x ) e ^{s i n (x)}}{( 2 + cos ( π ) x ) ^{2}}

\frac{d}{d x} (e^{s i n (x)}) = e^{s i n (x)} cos (x)

\frac{d}{d x} (2 + cos (π) x) = - 1

= \frac{e ^{s i n (x)} cos ( x ) ( 2 + cos ( π ) x ) - ( - 1 ) e ^{s i n (x)}}{( 2 + cos ( π ) x ) ^{2}}

Simplify

\frac{e ^{s i n (x)} cos ( x ) ( 2 + cos ( π ) x ) - ( - 1 ) e ^{s i n (x)}}{( 2 + cos ( π ) x ) ^{2}} : \frac{e ^{s i n (x)} cos ( x ) ( 2 - x ) + e ^{s i n (x)}}{( 2 - x ) ^{2}}

= \frac{e ^{s i n (x)} cos ( x ) ( 2 - x ) + e ^{s i n (x)}}{( 2 - x ) ^{2}}

\frac{d y}{d x}, y^{4} = x^{5}

\int t^{2} e^{4 t} d t

\int 9 x e^{6 x} d x

\frac{d}{d x} ((x^{2} + x)^{x})

x \to \infty lim (e^{p x} (a cos (q (x) x) + b sin (q (x) x)))

What is the derivative of (e^{sin(x})/(2+cos(pi)x)) ?
The derivative of (e^{sin(x})/(2+cos(pi)x)) is (e^{sin(x)}cos(x)(2-x)+e^{sin(x)})/((2-x)^2)
What is the first derivative of (e^{sin(x})/(2+cos(pi)x)) ?
The first derivative of (e^{sin(x})/(2+cos(pi)x)) is (e^{sin(x)}cos(x)(2-x)+e^{sin(x)})/((2-x)^2)