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Beliebt Rechnen >

derivative of 4x^3sec(7x)

Lösung

\frac{d}{d x} (4 x^{3} sec (7 x))

Lösung

4 (3 x^{2} sec (7 x) + sec (7 x) tan (7 x) \cdot 7 x^{3})

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} sec (7 x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{3} sec (7 x))

Wende die Produktregel an:

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

f = x^{3}, g = sec (7 x)

= 4 (\frac{d}{d x} (x^{3}) sec (7 x) + \frac{d}{d x} (sec (7 x)) x^{3})

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

\frac{d}{d x} (sec (7 x)) = sec (7 x) tan (7 x) \cdot 7

= 4 (3 x^{2} sec (7 x) + sec (7 x) tan (7 x) \cdot 7 x^{3})

Graph

Beliebte Beispiele

tangent sqrt(x^2+16),\at x=3

t an g e n t x^{2} + 16, at x = 3

integral of 1/3 x^3sqrt(9-x^2)

\int \frac{1}{3} x^{3} 9 - x^{2} d x

derivative of f(x)=(12)/((3x-4)^5)

\frac{d}{d x} f (x) = \frac{12}{( 3 x - 4 ) ^{5}}

integral of (-2)/(z^3)

\int \frac{- 2}{z ^{3}} d z

y^{''}+4y^'+5y=15x+e^{-x}

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 x + e^{- x}