Find the gradient at the point (3,-3,2) of the scaler field given by f=xy−4ze+35

Globokim8

Globokim8

Answered question

2020-12-16

Find the gradient at the point (3,-3,2) of the scaler field given by f=xy4ze+35

Answer & Explanation

Leonard Stokes

Leonard Stokes

Skilled2020-12-17Added 98 answers

The gradient is given by f=(dfdxdfdydfdz)
Now, (dfdx)=ddx(xy4ze+35)=ddx(xy)+ddx(4ze+35)=y (when taking the partial derivative with respect to x, all other yariables are treating as constants). Similarly,
dfdy=ddy(xy)+ddy(4ze+35)=x and dfdz=ddz(4ze)+ddz(xy+35)=4e Therefore, f=(y,x,4e) To find the gradient at(3,-3,2), plug in x=3,y=3,z=2 into(1): f(3,3,2)=(3,3,4e)

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