91影视

Given function is in three variable $$x$$, $$y$$ & $$z$$ and is defined by $$xe^{鈭�4z} \sin{y}$$

Since $$x$$ is the only variable here, the function which needs to be differentiated is only $$x$$. The rest part of $$xe^{鈭�4z} \sin{y}$$ acts as a constant i.e. $$e^{鈭�4z} \sin{y}$$. Now the given function $$xe^{鈭�4z} \sin{y}$$ is termed as $$kx$$ where $$k$$ is a constant,$$k= e^{鈭�4z} \sin{y}$$. Now we know the differentiation of $$kx$$ is $$k$$ i.e. the constant part only. Hence, the derivative of the function $$xe^{鈭�4z} \sin{y}$$ is $$e^{鈭�4z} \sin{y}$$ if $$x$$ is the variable and $$y$$ and $$z$$ are constants.

Similar to the step 2. Since $$y$$ is the only variable here, the function which needs to be differentiated is only $$\sin{y}$$. The rest part of $$xe^{鈭�4z} \sin{y}$$ acts as a constant i.e. $$xe^{鈭�4z}$$. Now the given function $$xe^{鈭�4z} \sin{y}$$ is termed as $$k\sin{y}$$ where $$k$$ is a constant,$$k= xe^{鈭�4z} $$. Now we know the differentiation of $$k\sin{y}$$ is $$k\cos{y}$$. Hence, the derivative of the function $$xe^{鈭�4z} \sin{y}$$ is $$xe^{鈭�4z} \cos{y}$$ if $$y$$ is the variable and $$x$$ and $$z$$ are constants.

Similar to the step 3. Since $$z$$ is the only variable here, the function which needs to be differentiated is only $$e^{-4z}$$. The rest part of $$xe^{鈭�4z} \sin{y}$$ acts as a constant i.e. $$x\sin{y}$$. Now the given function $$xe^{鈭�4z} \sin{y}$$ is termed as $$ke^{-4z}$$ where $$k$$ is a constant,$$k= x\sin{y} $$. Now we know the differentiation of $$ke^{-4z}$$ is $$-4ke^{-4z}$$. Hence, the derivative of the function $$xe^{鈭�4z} \sin{y}$$ is $$-4xe^{鈭�4z} \sin{y}$$ if $$z$$ is the variable and $$x$$ and $$y$$ are constants.

Since, in this case all the variables are constants, the given function acts as constant. Hence, we have to differentiate a constant function where constant $$k$$ (say) is $$xe^{鈭�4z} \sin{y}$$ We know that the differentiation of a constant function is zero. Hence, the differentiation of $$xe^{鈭�4z} \sin{y}$$ is $$0$$ when all the variables are constants.