derivative of x*tan(x^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot tan (x^{2}) + sec^{2} (x^{2}) \cdot 2 xx

Vereinfache

1 \cdot tan (x^{2}) + sec^{2} (x^{2}) \cdot 2 xx : tan (x^{2}) + 2 x^{2} sec^{2} (x^{2})

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

\frac{d}{d x} (-)

\frac{d x}{d t} = t + x^{2} t

\frac{\partial}{\partial y} (- e^{- x y})

t an g e n t f (x) = 7 x - x^{2}, at x = 1

(sin (2 t))^{^{'}}