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Hola.
![\frac{\partial \:}{\partial \:x}\left(fx=4\sen \left(x\right)\right)\quad \\ \\ f=4\frac{\partial \:}{\partial \:x}\left(x\sen \left(x\right)\right) \\ \\ Aplicamos \ regla \ del \ producto: \left(f\cdot g\right)^{'}=f^{'}\cdot g+f\cdot g^' \\ \\ \frac{\partial \:}{\partial \:x}\left(fx=4\sen \left(x\right)\right)\quad \\ \\ f=4\frac{\partial \:}{\partial \:x}\left(x\sen \left(x\right)\right) \\ \\ Aplicamos \ regla \ del \ producto: \left(f\cdot g\right)^{'}=f^{'}\cdot g+f\cdot g^' \\ \\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial+%5C%3A%7D%7B%5Cpartial+%5C%3Ax%7D%5Cleft%28fx%3D4%5Csen+%5Cleft%28x%5Cright%29%5Cright%29%5Cquad++%5C%5C++%5C%5C+f%3D4%5Cfrac%7B%5Cpartial+%5C%3A%7D%7B%5Cpartial+%5C%3Ax%7D%5Cleft%28x%5Csen+%5Cleft%28x%5Cright%29%5Cright%29+%5C%5C++%5C%5C+Aplicamos+%5C+regla+%5C+del+%5C+producto%3A+%5Cleft%28f%5Ccdot+g%5Cright%29%5E%7B%27%7D%3Df%5E%7B%27%7D%5Ccdot+g%2Bf%5Ccdot+g%5E%27+%5C%5C++%5C%5C+)
![f=4\left(\frac{\partial \:}{\partial \:x}\left(x\right)\sen \left(x\right)+\frac{\partial \:}{\partial \:x}\left(\sen \left(x\right)\right)x\right) \\ \\ \frac{\partial \:}{\partial \:x}\left(x\right)=1 \\ \\ \frac{\partial \:}{\partial \:x}\left(\sen \left(x\right)\right)=\cos \left(x\right) \\ \\ f=4\left(\frac{\partial \:}{\partial \:x}\left(x\right)\sen \left(x\right)+\frac{\partial \:}{\partial \:x}\left(\sen \left(x\right)\right)x\right) \\ \\ \frac{\partial \:}{\partial \:x}\left(x\right)=1 \\ \\ \frac{\partial \:}{\partial \:x}\left(\sen \left(x\right)\right)=\cos \left(x\right) \\ \\](https://tex.z-dn.net/?f=f%3D4%5Cleft%28%5Cfrac%7B%5Cpartial+%5C%3A%7D%7B%5Cpartial+%5C%3Ax%7D%5Cleft%28x%5Cright%29%5Csen+%5Cleft%28x%5Cright%29%2B%5Cfrac%7B%5Cpartial+%5C%3A%7D%7B%5Cpartial+%5C%3Ax%7D%5Cleft%28%5Csen+%5Cleft%28x%5Cright%29%5Cright%29x%5Cright%29+%5C%5C++%5C%5C+%5Cfrac%7B%5Cpartial+%5C%3A%7D%7B%5Cpartial+%5C%3Ax%7D%5Cleft%28x%5Cright%29%3D1+%5C%5C++%5C%5C+%5Cfrac%7B%5Cpartial+%5C%3A%7D%7B%5Cpartial+%5C%3Ax%7D%5Cleft%28%5Csen+%5Cleft%28x%5Cright%29%5Cright%29%3D%5Ccos+%5Cleft%28x%5Cright%29+%5C%5C++%5C%5C+)
![\ f=4\left(1\cdot \sin \left(x\right)+\cos \left(x\right)x\right) \\ \\ 1*x = x \\ \\ \boxed{Respuesta: \ f=4\left(x\cos \left(x\right)+\sin \left(x\right)\right)} \ f=4\left(1\cdot \sin \left(x\right)+\cos \left(x\right)x\right) \\ \\ 1*x = x \\ \\ \boxed{Respuesta: \ f=4\left(x\cos \left(x\right)+\sin \left(x\right)\right)}](https://tex.z-dn.net/?f=+%5C+f%3D4%5Cleft%281%5Ccdot+%5Csin+%5Cleft%28x%5Cright%29%2B%5Ccos+%5Cleft%28x%5Cright%29x%5Cright%29+%5C%5C++%5C%5C+1%2Ax+%3D+x+%5C%5C++%5C%5C+%5Cboxed%7BRespuesta%3A+%5C+f%3D4%5Cleft%28x%5Ccos+%5Cleft%28x%5Cright%29%2B%5Csin+%5Cleft%28x%5Cright%29%5Cright%29%7D)
¡Espero haberte ayudado, saludos... G.G.H!
¡Espero haberte ayudado, saludos... G.G.H!
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