What is the derivative of (e^x/(xcos(x))) ?

The derivative of (e^x/(xcos(x))) is (e^xxcos(x)-e^x(cos(x)-xsin(x)))/(x^2cos^2(x))

What is the first derivative of (e^x/(xcos(x))) ?

The first derivative of (e^x/(xcos(x))) is (e^xxcos(x)-e^x(cos(x)-xsin(x)))/(x^2cos^2(x))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) \frac{d y}{d x} = 0

\frac{d}{d x} (- x^{2} + 8 x - 12)

\frac{d}{d x} (2 x - 5)

y = x^{3} - 3 x + 5, (3, 23)

f (x) = \frac{x}{x ^{2} + 1}, at x = 0

What is the derivative of (e^x/(xcos(x))) ?
The derivative of (e^x/(xcos(x))) is (e^xxcos(x)-e^x(cos(x)-xsin(x)))/(x^2cos^2(x))
What is the first derivative of (e^x/(xcos(x))) ?
The first derivative of (e^x/(xcos(x))) is (e^xxcos(x)-e^x(cos(x)-xsin(x)))/(x^2cos^2(x))