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Beliebt Rechnen >

derivative of f(x(5x^2+3))

Lösung

\frac{d}{d x} (f (x) (5 x^{2} + 3))

Lösung

\frac{d}{d x} (f (x)) (5 x^{2} + 3) + 10 x f (x)

Schritte zur Lösung

\frac{d}{d x} (f (x) (5 x^{2} + 3))

Wende die Produktregel an:

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

f = f (x), g = 5 x^{2} + 3

= \frac{d}{d x} (f (x)) (5 x^{2} + 3) + \frac{d}{d x} (5 x^{2} + 3) f (x)

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= \frac{d}{d x} (f (x)) (5 x^{2} + 3) + 10 x f (x)

Beliebte Beispiele

integral of x^3sqrt(x^4+10)

\int x^{3} x^{4} + 10 d x

4y^{''}+4y^'+9y=0

4 y^{^{''}} + 4 y^{^{'}} + 9 y = 0

integral from 2 to 3 of 1/(x^2-1)

\int_{2}^{3} \frac{1}{x ^{2} - 1} d x

integral of (y-2)^2

\int (y - 2)^{2} d y

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

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