derivative of 5^{cos(x}+ln(x^2+1))

Lösung

\frac{d}{d x} (5^{c o s (x)} + ln (x^{2} + 1))

- ln (5) \cdot 5^{c o s (x)} sin (x) + \frac{2 x}{x ^{2} + 1}

Schritte zur Lösung

\frac{d}{d x} (5^{c o s (x)} + ln (x^{2} + 1))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (5^{c o s (x)}) + \frac{d}{d x} (ln (x^{2} + 1))

\frac{d}{d x} (5^{c o s (x)}) = - ln (5) \cdot 5^{c o s (x)} sin (x)

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

= - ln (5) \cdot 5^{c o s (x)} sin (x) + \frac{2 x}{x ^{2} + 1}

\int \frac{6 x}{( x ^{2} + 7 ) ^{2}} d x

\int 8 (x + 1) ln (x + 1) d x

\int w^{2} sin (10 w) d w

\frac{d}{d x} (2 cos (x) - x sin (x))

y^{^{''}} - 5 y^{^{'}} + 6 y = - sin (5 t)