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Beliebt Rechnen >

derivative f(x)=4x^2tan(x)

Lösung

ableitung von

f (x) = 4 x^{2} tan (x)

Lösung

4 (2 x tan (x) + sec^{2} (x) x^{2})

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} tan (x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2} tan (x))

Wende die Produktregel an:

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

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

= 4 (\frac{d}{d x} (x^{2}) tan (x) + \frac{d}{d x} (tan (x)) x^{2})

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

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

= 4 (2 x tan (x) + sec^{2} (x) x^{2})

Graph

Beliebte Beispiele

integral from 0 to 39 of 0.31sqrt(x)

\int_{0}^{39} 0.31 x d x

sum from n=1 to infinity of n(-1)^n

n = 1 \sum \infty n (- 1)^{n}

integral of 1/(8y)

\int \frac{1}{8 y} d y

integral of sec^2(x)tan^5(x)

\int sec^{2} (x) tan^{5} (x) d x

(dy)/(dx)+2xy=-x

\frac{d y}{d x} + 2 x y = - x