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Find the derivative

1. For each of the following functions, find the derivative. U“u— “at“ a. 1’0!) = (1 – 3z)‘“ + it sin(4-z)b. 90:) = tan6 2x c. h(z) = x! 1 + 3222 d. y = 25in (21—5) e. y=ln(x3-—3×2+5) 2. Consider the hyperbole with equation x2 — 322 = 1.a. Graph the hyperbole. There are two points on this curve where x = J37. Find their(1:, y) coordinates. (5 pts)b. Pick the point from part a) with positive y—coordinate, and find an equation of theline tangent to the hyperbola at this point. (10 pts)3. Use implicit differentiation to ?nd the derivative of y with respect to x ifx2 + :vczy2 + y3 = . (10 pts] 4. Use logarithmic differentiation to determine f ‘(x) if f(x) = 1%(10 pts}

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