(a) (b) (c) On this problem only, you MUST make a u-substitution and change to U's limits. On subsequent definite integrals you can choose to switch to u's limits or not, but use proper notation. *cos(x) sin²(x) dx √ √x (x³ + 2)dx √4x sin(x²) dx

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A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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A:

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A: By using derivative formula

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Q: 3. Find f. (a) f"(x) = x + 12x² %3D

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A: Given that f(x)= sinx and g(x)=x2. And we find (g0f)'(x). We know that d(xn)/dx = nxn-1.     Here i…

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A: We first find the derivatives

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A: So, Again, if , Then

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Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

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A: Given, f(t) = sin(t+tan√t) + ln(2t+1) fl(t)=?

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A: We can find f(x) as below, by finding the derivative.

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A: Solution of given question is followed by:

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A: Given, Select the true statement about substitution method:

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Q: Step 2 Now write the derivative in terms of x by recalling that u = x³ = x + 8. [eu] = (eu) du dx…

A: I have solved step by step in detail....go through the solution