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- 無名小子Lv 79 years ago
令 G(t)=∫ e^(t^2) dt

G '(t)=e^(t^2)

by chain rule

G'(x)=e^(t^2)*(dt/dx)

so

f(x)=∫ (從x到x^2) e^(t^2) dt

f '(x)=e^(x^2)^2*(x^2)'-e^(x^2)*(x)'

=(2x)*e^(x^4)-e^(x^2)

f '(0)=(2*0)*e^(0^4)-e^(0^2)

=0-1=-1

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- 興豪Lv 59 years ago
Set F(x)=∫[Ψ(x),φ(x)] f(t) dt ; F'(x) = f(φ(x))φ’(x) - f(Ψ(x))Ψ’(x)

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