10. Find the first derivative with respect to the independent variable for the following functions: (a)...
10. Find the first derivative with respect to the independent variable for the following functions: (a) f(x) = sinh(4x) (b) g(t) = cosh(t) sinh(t). 1 - cosh(r) (c) h(r) = 1 + cosh(r) (d) F(X) = tanh(e). (e) y = sinh--(VT). (Hint: Apply implicit differentiation to sinh(y) = VT.) 11. Use appropriate hyperbolic function substitutions to evaluate the following indef- inite integrals: dc (a) /+) Ke-10) (e)/() dx (b) dar James G., Modern Engineering Mathematics (5th ed.) 2015.: Exercise set...
Find the first derivative with respect to the domain variable for the following functions. 4. f(x) = (x - 2)(x² + 2x +4)
3. Find the indicated derivatives of the following functions without inte- grating. Make sure to fully justify your work! () ) (a) Let c E R da cos dt er+1 d tan(t) df (b) dr arctan(r) rt (c) H(r) 1+2+ dt; H"()
3. Find the indicated derivatives of the following functions without inte- grating. Make sure to fully justify your work! () ) (a) Let c E R da cos dt er+1 d tan(t) df (b) dr arctan(r) rt (c)...
Use logarithmic differentiation to find the derivative of y with respect to the given independent variable. t 3 y= 19t + 1 =
Please answer all, thank you in advance
With respect to the independent variable as indicated. Obtain the derivative of the following functions. y = sec 2t y = x Arcsin 2x Arc tan 2x Y x = e(cos2t + 2 sin 2t) y=xel
Find the derivative of y with respect to the independent variable. Select one: A. g* * 12 In gx + 1) + 1 in gx C. x(2 In 9x +1) DOX +7(2 in 9x) 2. E, none y-arte
Below are eight functions. Find the first derivative of each. Space is provided. Use good dark ink if you are returning this by a scanned version. All of the derivatives can be found by using combinations of the constant rule, power function rule and sum-difference rule. Do not use the product rule. It is not needed. The degree of difficulty (more or less) increases from (a-h). Be sure to show intermediate work. Check the scoring rubric to see how the points are awarded. For example, the first...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...
5. Use a substitution and an integration by parts to find each of the following indef- inite integrals: (b) | (cos(a) sin(a) esas) de (a) / ( (32 – 7) sin(5x + 2)) de (c) / (e* cos(e=)) dt (d) dr 6. Spot the error in the following calculation: S() will use integration by parts with 1 We wish to compute dr. For this dv du 1 dar = 1. This gives us dr by parts we find dr =...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)