Using the Laplace transform solve the following initial value problem x" - 2x + x = t - sint, x = x (t), x' (0) = x(0) = 0.

1. Find dy/dx = y' by logarithmic differentiation. (Must use logarithmic differentiation should express the answer in terms of x only but do not simplify. ) You (4x+5)² y= (x²+3) 2(x-3)x³

1. Candace tried to find the derivative of the function y = h(x)e-4f(x) but her group members disagreed with her result. What did she get right? What did she get wrong? Correct her y' = h'(x)e-4f(x) + h(x)e-4f(x) (-4) work. After figuring out her error, Candace attempted to check her solution by rearranging the right side of the equation y = h(x)e-4f(x) into a fraction and using the quotient rule to differentiate. Verify the correct solution using this method.

I am having some trouble with a calculas problem I was wondering if you could help. If F(x)=intergril of -1 to 2x sqrt of t^3+1 dt find F'(1)