derivative of x^2sin(xtan(x))

Lösung

\frac{d}{d x} (x^{2} sin (x) tan (x))

2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin (x) tan (x))

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

= 2 x sin (x) tan (x) + sin (x) (1 + sec^{2} (x)) x^{2}

y^{^{''}} + 4 y^{^{'}} - 5 = 0

h \to 0 lim (\frac{h}{h ^{2} + 7 h + 1})

\frac{d}{d x} (\frac{1 - 4 x}{2 + x})

im pl i c i t \frac{d y}{d x}, x y = y^{3}

\int \frac{2 v}{2 - 3 v ^{2}} d v