derivative of (3x^2tan(x)/(sec(x)))

Lösung

\frac{d}{d x} (\frac{3 x ^{2} tan ( x )}{sec ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} tan ( x )}{sec ( x )})

Vereinfache

\frac{3 x ^{2} tan ( x )}{sec ( x )} : 3 x^{2} tan (x) cos (x)

= \frac{d}{d x} (3 x^{2} tan (x) cos (x))

Entferne die Konstante:

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

= 3 \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)

= 3 (\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)

= 3 (2 x tan (x) cos (x) + cos (x) x^{2})

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

= 3 (x^{2} cos (x) + 2 x sin (x))

d er i v a t i v e sin (cos (tan (π x)))

\frac{d}{d x} ((x^{3} - x + 1)^{3})

x \to 2 + lim (\frac{x}{x ^{2} + 4})

x \to 7 lim (\frac{6 x}{x - 7})

\frac{d}{d x} (x^{- 9 c o s (x)})