MATH SOLVE

4 months ago

Q:
# Use part 1 of the fundamental theorem of calculus to find the derivative of the function. y = 5 u3 1 + u2 du 4 β 3x

Accepted Solution

A:

Looks like

[tex]y(x)=\displaystyle\int_5^{4-3x}u^3(1+u^2)\,\mathrm du[/tex]

in which case the FTC asserts that

[tex]\dfrac{\mathrm dy}{\mathrm dx}=(4-3x)^3(1+(4-3x)^2)\cdot\dfrac{\mathrm d(4-3x)}{\mathrm dx}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=-3(4-3x)^3(1+(4-3x)^2)[/tex]

[tex]y(x)=\displaystyle\int_5^{4-3x}u^3(1+u^2)\,\mathrm du[/tex]

in which case the FTC asserts that

[tex]\dfrac{\mathrm dy}{\mathrm dx}=(4-3x)^3(1+(4-3x)^2)\cdot\dfrac{\mathrm d(4-3x)}{\mathrm dx}[/tex]

[tex]\dfrac{\mathrm dy}{\mathrm dx}=-3(4-3x)^3(1+(4-3x)^2)[/tex]