d/(dθ)((h)(y(h,θ)-tan(θ)x(h,θ)+1))

Lösung

\frac{d}{d θ} ((h) (y (h, θ) - tan (θ) x (h, θ) + 1))

h (\frac{d}{d θ} (y (h, θ)) - (sec^{2} (θ) x (h, θ) + \frac{d}{d θ} (x (h, θ)) tan (θ)) + 0)

Schritte zur Lösung

\frac{d}{d θ} ((h) (y (h, θ) - tan (θ) x (h, θ) + 1))

Behandle

h

als Konstante

Entferne die Konstante:

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

= h \frac{d}{d θ} (y (h, θ) - tan (θ) x (h, θ) + 1)

Wende die Summen-/Differenzregel an:

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

= h (\frac{d}{d θ} (y (h, θ)) - \frac{d}{d θ} (tan (θ) x (h, θ)) + \frac{d}{d θ} (1))

\frac{d}{d θ} (tan (θ) x (h, θ)) = sec^{2} (θ) x (h, θ) + \frac{d}{d θ} (x (h, θ)) tan (θ)

\frac{d}{d θ} (1) = 0

= h (\frac{d}{d θ} (y (h, θ)) - (sec^{2} (θ) x (h, θ) + \frac{d}{d θ} (x (h, θ)) tan (θ)) + 0)

e x p an d f x \circ g (x - 1)

e x p an d c d (1 + ab + e)

e x p an d a b (x - h) + k

e x p an d f (x) d x (= 3 x^{2} - 8 x + 3)

e x p an d \frac{3 ( 805 - 25 )}{20}