The function h(x) = ex is the composition of the three functions f(x)=x, g(x)=e*, and k(x)...

Transcribed Image Text:

The function h(x) = √ex is the composition of the three functions f(x)=√x, g(x)=e*, and k(x) = x². Therefore, h(x) = (fogok)(x) = f(g(k(x))) = √√e². (Equation 1) dh a) Find by taking the derivative of Equation 1 by using quick methods. dx b) Now, find the derivative by using the chain rule in Liebniz notation. Does this agree the derivative found in part (a)? Chain rule in Liebniz notation: k(x)=x² Hint: g(k)= ek f(g)=√√g dh df dg dk dx dg dk dx The function h(x) = √ex is the composition of the three functions f(x)=√x, g(x)=e*, and k(x) = x². Therefore, h(x) = (fogok)(x) = f(g(k(x))) = √√e². (Equation 1) dh a) Find by taking the derivative of Equation 1 by using quick methods. dx b) Now, find the derivative by using the chain rule in Liebniz notation. Does this agree the derivative found in part (a)? Chain rule in Liebniz notation: k(x)=x² Hint: g(k)= ek f(g)=√√g dh df dg dk dx dg dk dx

Answer rating: 100% (QA)

a hx fog kx fgkxgkxkx fogxkx fexex1 fogkx fexex fogxkx fexex fgkxgkx... View the full answer