Calcolatrice delle derivate parziali
Calcolo delle derivate parziali passo dopo passo
Questa calcolatrice online calcola la derivata parziale della funzione, con i passi indicati. È possibile specificare qualsiasi ordine di integrazione.
Solution
Your input: find ∂∂x(2x2y−2x2+y3−2y2+2)
The derivative of a sum/difference is the sum/difference of derivatives:
∂∂x(2x2y−2x2+y3−2y2+2)=(∂∂x(2)−∂∂x(2x2)−∂∂x(2y2)+∂∂x(y3)+∂∂x(2x2y))Apply the constant multiple rule ∂∂x(c⋅f)=c⋅∂∂x(f) with c=2y and f=x2:
∂∂x(2x2y)+∂∂x(2)−∂∂x(2x2)−∂∂x(2y2)+∂∂x(y3)=2y∂∂x(x2)+∂∂x(2)−∂∂x(2x2)−∂∂x(2y2)+∂∂x(y3)Apply the power rule ∂∂x(xn)=n⋅x−1+n with n=2:
2y∂∂x(x2)+∂∂x(2)−∂∂x(2x2)−∂∂x(2y2)+∂∂x(y3)=2y(2x−1+2)+∂∂x(2)−∂∂x(2x2)−∂∂x(2y2)+∂∂x(y3)=4xy+∂∂x(2)−∂∂x(2x2)−∂∂x(2y2)+∂∂x(y3)Apply the constant multiple rule ∂∂x(c⋅f)=c⋅∂∂x(f) with c=2 and f=x2:
4xy−∂∂x(2x2)+∂∂x(2)−∂∂x(2y2)+∂∂x(y3)=4xy−(2∂∂x(x2))+∂∂x(2)−∂∂x(2y2)+∂∂x(y3)Apply the power rule ∂∂x(xn)=n⋅x−1+n with n=2:
4xy−2∂∂x(x2)+∂∂x(2)−∂∂x(2y2)+∂∂x(y3)=4xy−2(2x−1+2)+∂∂x(2)−∂∂x(2y2)+∂∂x(y3)=4xy−4x+∂∂x(2)−∂∂x(2y2)+∂∂x(y3)The derivative of a constant is 0:
4xy−4x−∂∂x(2y2)+∂∂x(2)+∂∂x(y3)=4xy−4x−(0)+∂∂x(2)+∂∂x(y3)The derivative of a constant is 0:
4xy−4x+∂∂x(2)+∂∂x(y3)=4xy−4x+(0)+∂∂x(y3)The derivative of a constant is 0:
4xy−4x+∂∂x(y3)=4xy−4x+(0)=4x(y−1)Thus, ∂∂x(2x2y−2x2+y3−2y2+2)=4x(y−1)
Answer: ∂∂x(2x2y−2x2+y3−2y2+2)=4x(y−1)