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

Lösung

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

2 x tan (x^{3} - x^{2}) cos (x) + (sec^{2} (x^{3} - x^{2}) cos (x) (3 x^{2} - 2 x) - sin (x) tan (x^{3} - x^{2})) x^{2}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

f = x^{2}, g = tan (x^{3} - x^{2}) cos (x)

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

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

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

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

y^{^{''}} + 3 y^{^{'}} = 10 sin (t)

t an g e n t y = 5 x - 4 x, (1, 1)

\int_{0}^{1} (∣ 3 x - 1 ∣ - 2 ∣ x ∣) d x

d er i v a t i v e - \frac{5}{4} t^{4} + 120 t^{2}

d er i v a t i v e (x^{2} + 1) \cdot e^{x - 1}