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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 Summary

Find the derivatives in these cases.

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