Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all cases, a, b, c are real constants, and y is a function of x.

Q: Let h(x) = x5 + 9x4 - 2x³-9x² + 4x Determine the third derivative of h. d³h dx³ =

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Q: y = 4x° + 4x at (1, 2)

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Q: Is the function f(2) = -2(xy+x)+i(x² – 2y – y) differentiable? If it is, find it's derivative.

A: Consider the given function.

Q: Find the derivative of  g(z) = 4z7-3z-7+9x

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Q: Differentiate. f'(x) = f(x) = ax + b cx + d

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Q: Find the derivative of f (x) = 3x2.e3x2 A 6x2. e3x2 + e3x² 3x2. e 3x² + 6x - e 3x2 ©) 18x3. e3x2 +…

A: Derivative

Q: Find all complementary functions of the equation xy" - 2y'=0, x>0 1, x² x₁ x³ a. b. C. d. x, x(Inx)²…

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Q: Let f(x)= ax'+x² + bx +6 where a and b are real numbers, and f(2)=3. Find the value of f(-2).

A: f(-2) = 17  The detailed solution is as follows below:

Q: Simplify the expression xyz + x’y + x’y’

A: We have to simplify the expression xyz+x'y+x'y'.