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Beliebt Rechnen >

derivative of (2x^2tan(x)/(sec(x)))

Lösung

\frac{d}{d x} (\frac{2 x ^{2} tan ( x )}{sec ( x )})

Lösung

2 (x^{2} cos (x) + 2 x sin (x))

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2} tan ( x )}{sec ( x )})

Vereinfache

\frac{2 x ^{2} tan ( x )}{sec ( x )} : 2 x^{2} tan (x) cos (x)

= \frac{d}{d x} (2 x^{2} tan (x) cos (x))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x^{2} tan (x) cos (x))

Wende die Produktregel an:

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

f = x^{2}, g = tan (x) cos (x)

= 2 (\frac{d}{d x} (x^{2}) tan (x) cos (x) + \frac{d}{d x} (tan (x) cos (x)) x^{2})

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

\frac{d}{d x} (tan (x) cos (x)) = cos (x)

= 2 (2 x tan (x) cos (x) + cos (x) x^{2})

cos (x) tan (x) = sin (x)

= 2 (x^{2} cos (x) + 2 x sin (x))

Graph

Beliebte Beispiele

integral of sec^2(θ)tan^3(θ)

\int sec^{2} (θ) tan^{3} (θ) d θ

integral of ((x+2))/(sqrt(x))

\int \frac{( x + 2 )}{x} d x

limit as x approaches 0 of x^2ln|x|

x \to 0 lim (x^{2} ln ∣ x ∣)

(\partial)/(\partial x)(y^{x^y})

\frac{\partial}{\partial x} (y^{x^{y}})

y^{''}-4y^'+4y=t^{-4}e^{2t}

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{- 4} e^{2 t}