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Kalkulator pochodnej częściowej

Obliczanie pochodnych cząstkowych krok po kroku

Ten kalkulator online obliczy pochodną cząstkową funkcji, z pokazanymi krokami. Można określić dowolną kolejność całkowania.

Enter a function:

Enter the order of integration:

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

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Solution

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

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

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

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

y(2x2y)+y(2)y(2x2)y(2y2)+y(y3)=2x2y(y)+y(2)y(2x2)y(2y2)+y(y3)

Apply the power rule y(yn)=ny1+n with n=1, in other words y(y)=1:

2x2y(y)+y(2)y(2x2)y(2y2)+y(y3)=2x21+y(2)y(2x2)y(2y2)+y(y3)

The derivative of a constant is 0:

2x2y(2x2)+y(2)y(2y2)+y(y3)=2x2(0)+y(2)y(2y2)+y(y3)

Apply the constant multiple rule y(cf)=cy(f) with c=2 and f=y2:

2x2y(2y2)+y(2)+y(y3)=2x2(2y(y2))+y(2)+y(y3)

Apply the power rule y(yn)=ny1+n with n=2:

2x22y(y2)+y(2)+y(y3)=2x22(2y1+2)+y(2)+y(y3)=2x24y+y(2)+y(y3)

The derivative of a constant is 0:

2x24y+y(2)+y(y3)=2x24y+(0)+y(y3)

Apply the power rule y(yn)=ny1+n with n=3:

2x24y+y(y3)=2x24y+(3y1+3)=2x2+3y24y

Thus, y(2x2y2x2+y32y2+2)=2x2+3y24y

Answer: y(2x2y2x2+y32y2+2)=2x2+3y24y