derivative of (e^{5x^2-2x}/(cot(7^x)))

Lösung

\frac{d}{d x} (\frac{e ^{5 x^{2} - 2 x}}{cot ( 7 ^{x} )})

e^{5 x^{2} - 2 x} (10 x - 2) tan (7^{x}) + sec^{2} (7^{x}) \cdot 7^{x} ln (7) e^{5 x^{2} - 2 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{5 x^{2} - 2 x}}{cot ( 7 ^{x} )})

Vereinfache

\frac{e ^{5 x^{2} - 2 x}}{cot ( 7 ^{x} )} : e^{5 x^{2} - 2 x} tan (7^{x})

= \frac{d}{d x} (e^{5 x^{2} - 2 x} tan (7^{x}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{5 x^{2} - 2 x}, g = tan (7^{x})

= \frac{d}{d x} (e^{5 x^{2} - 2 x}) tan (7^{x}) + \frac{d}{d x} (tan (7^{x})) e^{5 x^{2} - 2 x}

\frac{d}{d x} (e^{5 x^{2} - 2 x}) = e^{5 x^{2} - 2 x} (10 x - 2)

\frac{d}{d x} (tan (7^{x})) = sec^{2} (7^{x}) \cdot 7^{x} ln (7)

= e^{5 x^{2} - 2 x} (10 x - 2) tan (7^{x}) + sec^{2} (7^{x}) \cdot 7^{x} ln (7) e^{5 x^{2} - 2 x}

\frac{d}{d x} (8 cos^{3} (x))

\frac{\partial}{\partial x} (\frac{1}{sin ( x ^{2} - y ^{2} )})

y^{^{''}} + a = 0

f^{^{'}} (x) = x^{4}

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