derivative (4+sec(θ))sin(θ)

Lösung

ableitung von

(4 + sec (θ)) sin (θ)

cos (θ) (4 + sec (θ)) + tan^{2} (θ)

Schritte zur Lösung

\frac{d}{d θ} ((4 + sec (θ)) sin (θ))

Wende die Produktregel an:

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

f = 4 + sec (θ), g = sin (θ)

= \frac{d}{d θ} (4 + sec (θ)) sin (θ) + \frac{d}{d θ} (sin (θ)) (4 + sec (θ))

\frac{d}{d θ} (4 + sec (θ)) = sec (θ) tan (θ)

\frac{d}{d θ} (sin (θ)) = cos (θ)

= sec (θ) tan (θ) sin (θ) + cos (θ) (4 + sec (θ))

Vereinfache

sec (θ) tan (θ) sin (θ) + cos (θ) (4 + sec (θ)) : cos (θ) (4 + sec (θ)) + tan^{2} (θ)

= cos (θ) (4 + sec (θ)) + tan^{2} (θ)

\int_{1}^{5} \frac{6}{x} d x

\frac{d}{d x} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

\int_{2}^{5} x d x

n = 1 \sum \infty ln (1)

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