derivative (5x^2tan(x))/(sec(x))

Lösung

ableitung von

\frac{5 x ^{2} tan ( x )}{sec ( x )}

5 (x^{2} cos (x) + 2 x sin (x))

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x ^{2} tan ( x )}{sec ( x )})

Vereinfache

\frac{5 x ^{2} tan ( x )}{sec ( x )} : 5 x^{2} tan (x) cos (x)

= \frac{d}{d x} (5 x^{2} tan (x) cos (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x^{2} tan (x) cos (x))

Wende die Produktregel an:

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

f = x^{2}, g = tan (x) cos (x)

= 5 (\frac{d}{d x} (x^{2}) tan (x) cos (x) + \frac{d}{d x} (tan (x) cos (x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (tan (x) cos (x)) = cos (x)

= 5 (2 x tan (x) cos (x) + cos (x) x^{2})

cos (x) tan (x) = sin (x)

= 5 (x^{2} cos (x) + 2 x sin (x))

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

a re a 2 - x^{2}, x^{2}

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + 9 x z - 12)

d er i v a t i v e 3 t - 3 e^{t}

\int tan^{2} (x) sec^{2} (x) d x