derivative of arcsinh(5x^3-4x^2+11)

Lösung

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

\frac{15 x ^{2} - 8 x}{25 x ^{6} - 40 x ^{5} + 16 x ^{4} + 110 x ^{3} - 88 x ^{2} + 122}

Schritte zur Lösung

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

Wende die Kettenregel an:

\frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} \frac{d}{d x} (5 x^{3} - 4 x^{2} + 11)

= \frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} \frac{d}{d x} (5 x^{3} - 4 x^{2} + 11)

\frac{d}{d x} (5 x^{3} - 4 x^{2} + 11) = 15 x^{2} - 8 x

= \frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} (15 x^{2} - 8 x)

Vereinfache

\frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} (15 x^{2} - 8 x) : \frac{15 x ^{2} - 8 x}{25 x ^{6} - 40 x ^{5} + 16 x ^{4} + 110 x ^{3} - 88 x ^{2} + 122}

= \frac{15 x ^{2} - 8 x}{25 x ^{6} - 40 x ^{5} + 16 x ^{4} + 110 x ^{3} - 88 x ^{2} + 122}

t an g e n t f (x) = 2 x - 1 + \frac{6}{x}, at x = 2

\frac{\partial}{\partial x} (A (e^{2 x} + 2 e^{2 x} x))

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\frac{\partial}{\partial x} (x^{2} + y^{2} - z^{2})

\int_{- 2}^{- 1} \frac{4}{x ^{2}} d x