(\partial)/(\partial x)((14+17x)y^{tan(x)})

Lösung

\frac{\partial}{\partial x} ((14 + 17 x) y^{t a n (x)})

17 y^{t a n (x)} + y^{t a n (x)} ln (y) sec^{2} (x) (14 + 17 x)

Schritte zur Lösung

\frac{\partial}{\partial x} ((14 + 17 x) y^{t a n (x)})

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = 14 + 17 x, g = y^{t a n (x)}

= \frac{\partial}{\partial x} (14 + 17 x) y^{t a n (x)} + \frac{\partial}{\partial x} (y^{t a n (x)}) (14 + 17 x)

\frac{\partial}{\partial x} (14 + 17 x) = 17

\frac{\partial}{\partial x} (y^{t a n (x)}) = y^{t a n (x)} ln (y) sec^{2} (x)

= 17 y^{t a n (x)} + y^{t a n (x)} ln (y) sec^{2} (x) (14 + 17 x)

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

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

d er i v a t i v e g (x) = ln (3 x)

d er i v a t i v e 9 x^{\frac{1}{3}} + \frac{9}{2} x^{\frac{4}{3}}

\frac{\partial}{\partial x} (- x e^{(x y)})