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Beliebt Rechnen >

derivative of tan(xln(x))

Lösung

\frac{d}{d x} (tan (x) ln (x))

Lösung

sec^{2} (x) ln (x) + \frac{tan ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (tan (x) ln (x))

Wende die Produktregel an:

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

f = tan (x), g = ln (x)

= \frac{d}{d x} (tan (x)) ln (x) + \frac{d}{d x} (ln (x)) tan (x)

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

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

= sec^{2} (x) ln (x) + \frac{1}{x} tan (x)

\frac{1}{x} tan (x) = \frac{tan ( x )}{x}

= sec^{2} (x) ln (x) + \frac{tan ( x )}{x}

Graph

Beliebte Beispiele

limit as x approaches 3 of 4x^3-3x^2+x-5

x \to 3 lim (4 x^{3} - 3 x^{2} + x - 5)

tangent-8sin(x)

t an g e n t - 8 sin (x)

derivative of x^4+2x^2+1

\frac{d}{d x} (x^{4} + 2 x^{2} + 1)

d/(dt)((cos(t))/t)

\frac{d}{d t} (\frac{cos ( t )}{t})

integral from 0 to 1 of x^2e^{-x}

\int_{0}^{1} x^{2} e^{- x} d x