1. Find the derivative for the function f(x) = 2e^x - 8^x 2. Find the derivative for the function f(z) = z^5 - e^z ln z 3. Find the tangent line to f(x) = 7^x + 4e^x at x = 0 4. Determine if G(z) = (z - 6)ln z is increasing or decreasing at the following points. (a) z=1 (b) z=5 (c) z=20 5. Find the derivative for the function f(x) = (x + 1)^x 6. Find the derivative for the function f(x) = (x)^{x+1} 7. Find the derivative for the function f(x) = (sqrt{x})^x 8. Find dy/dx for sqrt{3x^2 + 1}(3x^4 + 1)^3 9. Find dy/dx for y = 3x^{3x}
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Find the derivative for the function $f(x) = xe^x$. Using the product rule, we have: $$f'(x) = (1)(e^x) + (x)(e^x) = e^x(x+1)$$ Show more…
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Sri K.
1) differentiate the function f(x) = 2^6 2) differentiate the function g(x) = (7/6)x^2 - 4x + 16 3) Differentiate the function g(x) = x^2(1 - 4x) 4) Differentiate the function g(t) = 4t^(-3/8) 5) Differentiate the function F(r) = 5/r^3 6) Differentiate the function R(a) = (3a + 1)^2 7) Differentiate the function h(t) = 8√t - 8e^t 8) Differentiate the function y = (5x^2 + 5x + 5) / √x 9) Find an equation of the tangent line to the curve at the given point. y = 6ex + x, (0, 6) 10) Find the first and second derivative of the function. Check to see that your answers are reasonable by comparing the graphs of f, f', and f''. f(x) = ex - x^7
1) Find an equation of a line that is tangent to the graph of f and parallel to the given line. Function: Line: f(x) = x^3 12x - y + 6 = 0 y = (smaller y-intercept) y = (larger y-intercept) 2) The limit represents f'(c) for a function f(x) and a number c. Find f(x) and c. lim x→1 (8/x - 8)/(x - 1) f(x) = c = 3) Identify a function f that has the given characteristics. Then sketch the function. f(3) = 10 f'(x) = 2, -∞ < x < ∞ f(x) = 4) Evaluate f(3) and f(3.1) and use the results to approximate f'(3). (Round your answer to one decimal place.) f(x) = x(8 - x) f'(3) ≈ 5) Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the derivative does not exist at c, enter UNDEFINED.) f(x) = x^3 + 2x^2 + 7, c = -2 f'(-2) = 6) Describe the x-values at which the function is differentiable. (Enter your answer using interval notation.) y = x^2/(x^2 - 36) 7) Consider the following function. f(x) = |x - 8| Find the derivative from the left at x = 8. If it does not exist, enter NONE. Find the derivative from the right at x = 8. If it does not exist, enter NONE. Is the function differentiable at x = 8? Yes or No
Carson M.
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