derivative f(x)=(4x^2tan(x))/(sec(x))

Lösung

ableitung von

f (x) = \frac{4 x ^{2} tan ( x )}{sec ( x )}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{2} tan ( x )}{sec ( x )})

Vereinfache

\frac{4 x ^{2} tan ( x )}{sec ( x )} : 4 x^{2} tan (x) cos (x)

= \frac{d}{d x} (4 x^{2} tan (x) cos (x))

Entferne die Konstante:

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

= 4 \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)

= 4 (\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)

= 4 (2 x tan (x) cos (x) + cos (x) x^{2})

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

= 4 (x^{2} cos (x) + 2 x sin (x))

x \to - 2 lim (- 0.8)

x d y - y d x = (2 x^{2} - 3) d x

t a y l or \frac{3}{x ^{2} - x - 2}

\int_{1}^{3} ln (2 x) d x

x \to π lim (5)