derivative of f(x)=(2x-6)^2(x^2+x+1)^2

Lösung

\frac{d}{d x} f (x) = (2 x - 6)^{2} (x^{2} + x + 1)^{2}

f (x) = \frac{4 x ^{7}}{7} - \frac{8 x ^{6}}{3} + 2 x^{4} + \frac{64 x ^{3}}{3} + 24 x^{2} + 36 x + c_{1}

Schritte zur Lösung

\frac{df}{d x} = (2 x - 6)^{2} (x^{2} + x + 1)^{2}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

f (x) = \int (2 x - 6)^{2} (x^{2} + x + 1)^{2} d x

\int (2 x - 6)^{2} (x^{2} + x + 1)^{2} d x = \frac{4 x ^{7}}{7} - \frac{8 x ^{6}}{3} + 2 x^{4} + \frac{64 x ^{3}}{3} + 24 x^{2} + 36 x + c_{1}

f (x) = \frac{4 x ^{7}}{7} - \frac{8 x ^{6}}{3} + 2 x^{4} + \frac{64 x ^{3}}{3} + 24 x^{2} + 36 x + c_{1}

\frac{d}{d x} (\frac{4}{sin ( x ) + cos ( x )})

\int cos (x) - 9 sin (x) d x

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a re a f (x) = x + 3, [0, 9]

x \to 2 \cdot π lim (ln (cos (x)))