derivative of (0.07e^x/(sin(x)))

Lösung

\frac{d}{d x} (\frac{0.07 e ^{x}}{sin ( x )})

0.07 (e^{x} csc (x) - e^{x} cot (x) csc (x))

Schritte zur Lösung

\frac{d}{d x} (\frac{0.07 e ^{x}}{sin ( x )})

Vereinfache

\frac{0.07 e ^{x}}{sin ( x )} : 0.07 e^{x} csc (x)

= \frac{d}{d x} (0.07 e^{x} csc (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.07 \frac{d}{d x} (e^{x} csc (x))

Wende die Produktregel an:

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

f = e^{x}, g = csc (x)

= 0.07 (\frac{d}{d x} (e^{x}) csc (x) + \frac{d}{d x} (csc (x)) e^{x})

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= 0.07 (e^{x} csc (x) + (- cot (x) csc (x)) e^{x})

Vereinfache

= 0.07 (e^{x} csc (x) - e^{x} cot (x) csc (x))

\frac{d x}{d t} = x^{2} - x

\int \frac{1}{x ^{2} + 64} d x

\frac{d}{d x} (\frac{x + 1}{e ^{x}})

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x - 5}{( x + 1 ) ^{2}}

t = \frac{1 - y ^{2}}{y ^{^{'}}}