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Beliebt Rechnen >

(\partial)/(\partial x)(arctan(xsqrt(t)))

Lösung

\frac{\partial}{\partial x} (arctan (x t))

Lösung

\frac{t}{x ^{2} t + 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (arctan (x t))

Behandle

t

als Konstante

Wende die Kettenregel an:

\frac{1}{( x t ) ^{2} + 1} \frac{\partial}{\partial x} (x t)

= \frac{1}{( x t ) ^{2} + 1} \frac{\partial}{\partial x} (x t)

\frac{\partial}{\partial x} (x t) = t

= \frac{1}{( x t ) ^{2} + 1} t

Vereinfache

\frac{1}{( x t ) ^{2} + 1} t : \frac{t}{x ^{2} t + 1}

= \frac{t}{x ^{2} t + 1}

Beliebte Beispiele

derivative y=x^2+2

d er i v a t i v e y = x^{2} + 2

derivative of 4x-8

\frac{d}{d x} (4 x - 8)

derivative f(θ)=(sec(θ))/(1+sec(θ))

d er i v a t i v e f (θ) = \frac{sec ( θ )}{1 + sec ( θ )}

tangent f(x)=4x^2+7x

t an g e n t f (x) = 4 x^{2} + 7 x

integral of 1/(u^2-4)

\int \frac{1}{u ^{2} - 4} d u