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Beliebt Rechnen >

(\partial)/(\partial x)(k(1+ae^{-b(x,w,t)x})(1+cos(wt)))

Lösung

\frac{\partial}{\partial x} (k (1 + a e^{- b (x, w, t) x}) (1 + cos (wt)))

Lösung

k (1 + cos (wt)) (0 + a e^{- b (x, w, t) x} (- (\frac{\partial}{\partial x} (b (x, w, t)) x + 1 \cdot b (x, w, t))))

Schritte zur Lösung

\frac{\partial}{\partial x} (k (1 + a e^{- b (x, w, t) x}) (1 + cos (wt)))

Behandle

a, k, w, t

als Konstanten

Entferne die Konstante:

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

= k (1 + cos (wt)) \frac{\partial}{\partial x} (1 + a e^{- b (x, w, t) x})

Wende die Summen-/Differenzregel an:

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

= k (1 + cos (wt)) (\frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (a e^{- b (x, w, t) x}))

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (a e^{- b (x, w, t) x}) = a e^{- b (x, w, t) x} (- (\frac{\partial}{\partial x} (b (x, w, t)) x + 1 \cdot b (x, w, t)))

= k (1 + cos (wt)) (0 + a e^{- b (x, w, t) x} (- (\frac{\partial}{\partial x} (b (x, w, t)) x + 1 \cdot b (x, w, t))))

Beliebte Beispiele

derivative of (7x+4^2)

\frac{d}{d x} ((7 x + 4)^{2})

integral of 7/(xsqrt(4-49ln^2(x)))

\int \frac{7}{x 4 - 49 ln ^{2} ( x )} d x

integral of 3x(sqrt(5-x))

\int 3 x (5 - x) d x

y^{''}+9y=tan(3x)

y^{^{''}} + 9 y = tan (3 x)

integral of 1/(sqrt(12x-9x^2))

\int \frac{1}{12 x - 9 x ^{2}} d x