Question

Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x t3 t5 dt 0

Answer 1

Using the fundamental theorem of calculas the derivative of function g(x)=$xt^{3}+t^{5}$ at x=0 is $t^{3}$.

Given a function g(x)=$xt^{3}+t^{5}$.

We are required to find the derivative of the function g(x) at x=0.

Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.

g(x)=$xt^{3}+t^{5}$

Differentiating with respect to x.

d g(x)/dx=$t^{3}$+0  [Differentiation of x is 1 and differentiation of constant is 0]

=$t^{3}$

Hence using the fundamental theorem of calculas the derivative of function g(x)= $xt^{3}+t^{5}$ at x=0 is $t^{3}$.

The function given in the question is incomplete. The right function will be g(x)=$xt^{3}+t^{5}$.

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