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Beliebt Rechnen >

derivative of x^2tan(xy)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Beliebte Beispiele

derivative of (3x+1/(7x+5))

\frac{d}{d x} (\frac{3 x + 1}{7 x + 5})

derivative of (x^x/(sin(x)))

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

(dy)/(dx)=k*y^2

\frac{d y}{d x} = k \cdot y^{2}

(dy)/(dx)= 1/(1+x)

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

derivative f(x)=-12x^2+400x-3800

d er i v a t i v e f (x) = - 12 x^{2} + 400 x - 3800