Math

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 Discuss on the forum. No need to submit. Find /dx (x^3+y^3)where = g(x).

 Discuss on the forum. But do not submit. Find /dx (x^2 y)where = g(x).

 Find /dx (sin y+y cos x)where = g(x).

 Find y/dxby implicit differentiation. oot(x)-root(y) = 8.

 Find x/dtby implicit differentiation. -root(t) = t x.

 Find y/dxby implicit differentiation. oot (x y)+x y^2 = 4. [very long]

 Find y/dx |_(x = 3, y = 2)by implicit differentiation of ^4+y^4 = 97. What is the geometric meaning of y/dx |_(x = 3, y = 2)?

 Find an equation of the tangent line to the circle: ^2+y^2 = 25at the point -3, 4). Then graph the line together with the circle. In order to graph equations, you need to solve them for http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7By%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15. To graph ^2+y^2 = 25, plot = root (25-x^2)and =-root (25-x^2).

 Find an equation of the tangent line to the astroid: x^(2))^(1/3)+(y^(2))^(1/3) = 4at the point -3 root(3),1).

ttp://calculus.sfsu.edu/latexrender/pictures/824746d028384b64bd93ba0a49a8ec7a.png

 Find an equation of the tangent line to the hyperbola: ^(2)-2 y^(2) = 1at the point a,b).

ttp://calculus.sfsu.edu/latexrender/pictures/4e5fc4c5dda366a7e6e1205ecd4b5724.png

 Do not submit but please discuss it .You may earn valuable participation points. Using the theorem about the derivative of an inverse, show that for positive integers http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bm%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15and > 0, (x)^(1/m))' = 1/m x^(1/m-1).

 Do not submit but please discuss it Nairobi and Rio are located on the Tropic of Capricorn. On December 21, that is on the day of the Solstice at midday the Sun is vertical. How fast is the shadow of a pole 3 meters tall increasing at (a) midday, (b) at dusk?