What is the derivative of (e^x-cos(x)/(ln(x))) ?

The derivative of (e^x-cos(x)/(ln(x))) is (e^xxln(x)+xln(x)sin(x)-e^x+cos(x))/(xln^2(x))

What is the first derivative of (e^x-cos(x)/(ln(x))) ?

The first derivative of (e^x-cos(x)/(ln(x))) is (e^xxln(x)+xln(x)sin(x)-e^x+cos(x))/(xln^2(x))

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\frac{d}{d x} (\frac{e ^{x} - cos ( x )}{ln ( x )})

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

Solution steps

\frac{d}{d x} (\frac{e ^{x} - cos ( x )}{ln ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} - cos ( x ) ) ln ( x ) - \frac{d}{d x} ( ln ( x ) ) ( e ^{x} - cos ( x ) )}{( ln ( x ) ) ^{2}}

\frac{d}{d x} (e^{x} - cos (x)) = e^{x} + sin (x)

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

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

Simplify

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

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

\int_{0}^{1} x + 1 d x

\int \frac{6 x ^{3} + 5 x ^{2} - 46 x - 39}{x ^{2} - 9} d x

3 x d y - 2 y d x = 0

\int (x - \frac{1}{x})^{3} d x

\int \frac{1}{( x - 3 ) ^{2} + 3} d x

What is the derivative of (e^x-cos(x)/(ln(x))) ?
The derivative of (e^x-cos(x)/(ln(x))) is (e^xxln(x)+xln(x)sin(x)-e^x+cos(x))/(xln^2(x))
What is the first derivative of (e^x-cos(x)/(ln(x))) ?
The first derivative of (e^x-cos(x)/(ln(x))) is (e^xxln(x)+xln(x)sin(x)-e^x+cos(x))/(xln^2(x))