derivative x^3csc(x)

Lösung

ableitung von

x^{3} csc (x)

3 x^{2} csc (x) - x^{3} cot (x) csc (x)

Schritte zur Lösung

\frac{d}{d x} (x^{3} csc (x))

Wende die Produktregel an:

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

f = x^{3}, g = csc (x)

= \frac{d}{d x} (x^{3}) csc (x) + \frac{d}{d x} (csc (x)) x^{3}

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= 3 x^{2} csc (x) + (- cot (x) csc (x)) x^{3}

Vereinfache

= 3 x^{2} csc (x) - x^{3} cot (x) csc (x)

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

\int \frac{1 - sin ^{3} ( x )}{sin ^{2} ( x )} d x

\frac{d}{d x} (\frac{2 x ^{2} - 3 x + 1}{x})

s l o p e x^{2} + x y + 2 y^{2} = 28, (2, 3)

t^{2} y^{^{''}} + 7 t y^{^{'}} + 10 y = 0