Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js

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.

Enter a function:

Enter the order of integration:

Hint: type x^2,y to calculate , or enter x,y^2,x to find .

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: find x(2x2y2x2+y32y2+2)

The derivative of a sum/difference is the sum/difference of derivatives:

x(2x2y2x2+y32y2+2)=(x(2)x(2x2)x(2y2)+x(y3)+x(2x2y))

Apply the constant multiple rule x(cf)=cx(f) with c=2y and f=x2:

x(2x2y)+x(2)x(2x2)x(2y2)+x(y3)=2yx(x2)+x(2)x(2x2)x(2y2)+x(y3)

Apply the power rule x(xn)=nx1+n with n=2:

2yx(x2)+x(2)x(2x2)x(2y2)+x(y3)=2y(2x1+2)+x(2)x(2x2)x(2y2)+x(y3)=4xy+x(2)x(2x2)x(2y2)+x(y3)

Apply the constant multiple rule x(cf)=cx(f) with c=2 and f=x2:

4xyx(2x2)+x(2)x(2y2)+x(y3)=4xy(2x(x2))+x(2)x(2y2)+x(y3)

Apply the power rule x(xn)=nx1+n with n=2:

4xy2x(x2)+x(2)x(2y2)+x(y3)=4xy2(2x1+2)+x(2)x(2y2)+x(y3)=4xy4x+x(2)x(2y2)+x(y3)

The derivative of a constant is 0:

4xy4xx(2y2)+x(2)+x(y3)=4xy4x(0)+x(2)+x(y3)

The derivative of a constant is 0:

4xy4x+x(2)+x(y3)=4xy4x+(0)+x(y3)

The derivative of a constant is 0:

4xy4x+x(y3)=4xy4x+(0)=4x(y1)

Thus, x(2x2y2x2+y32y2+2)=4x(y1)

Answer: x(2x2y2x2+y32y2+2)=4x(y1)