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Find the derivative

Find the derivative;

G(v)= (v^3-1)/(v^3+1)

Find the limit;

lim(sin3x)/(sin5x)
x->0

Find the derivative;

R(w)= (cosw)/(1-sinw)

H(o)=(1+seco)/(1-seco)

Find the derivative;

F(x)= cos(3x^2)+{cos^2}3x

N(x)=(sin5x-cos5x)^5

"Assume that the equation determines a differentiable function f such that y=f(x), find y'."

5x^2-xy-4y^2=0

x^4+4x^2y^2-3xy^2+2x=0

"Assume all variables are functions of t."

If S=z^3 and dz/dt=-2 when z=3, find dS/dt.

Find the extrema of f on the given interval.

f(x)=3x^2-10x+7; [-1,3]

"Show that f satisfies the hypotheses of Rolle's Theorem on [a,b] and find all numbers c in (a,b) such that f'(c)=0."

f(x)=5-12x-2x^2; [-7,1]

"Determine whether f satisfies the hypotheses of the mean value theorem on [a,b] and if so, find all numbers c in (a,b) such that f(b)-f(a)=f'(c)(b-a)."

f(x)=3x^2+x-4; [1,5]

Find the extrema and sketch the graph of f.

f(x)=(2x-5)/(x+3)

Solution Preview

Dear Student
Please find the attachment for the solution.

Calculus problems
Some of the questions I can't understand what they are asking. Those are in quotes. I also need all the calculations for all the problems so I can see how you got the answers. Thanks!

Find the derivative;

Using the quotient rule, we have

Find the limit;

as the value of each of the limits involved is equal to 1.

Find the derivative;

Using the quotient rule, we have

Find the derivative

Find the derivative;

Here we use the chain rule or function of a function rule to differentiate.

Again, we use the chain rule here.

"Assume that the equation determines a differentiable function f such that y=f(x), find y'."
The following functions are called implicit functions. It is difficult to solve for one of the variables involved to be expressed in terms of the other variable, in which case the differentiation is difficult. The above ...

Solution Summary

The expert finds the derivatives in these cases.

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