Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3 +3CSC2X- 5√x - 4π   F(X) = (5- 3x2 + X4)/ X4 Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an initial condition of f(3) = 2

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

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Q: Find the derivative of the following functions: (a) f(x) = 6x² — 83 - 12/20 2-4√x (b) y = 6 cos(3x)…

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Q: Find g'(x) if g(x) = 4x e 3x g'(x) =

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Q: The function g(x) = 12x2² - sin x is the first derivative of f(x). If f(0) = -2, what is the value…

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Q: From the basic definition of complex integration, evaluate the integral o f(z) dz, where C is the…

A: Let us parametrize C: the unit circle enclosing the origin by z=eit. Here, f(z)=z2. Now, we need to…

Q: Complete the table by finding the function g(x) and the derivative of g(x) and h(x), if possible.…

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Q: 2a5 Given that f(x) = and values h(-1) =-3. h'(-1) = 7, find f(-1) AND f'(-1). h(x) %3D Show your…

A: f(x)=2x5h(x), and values h(-1)=-3, h'(-1)=7

Q: Solve the equation f"(x) = 0

A: It is given that,   f(x)=x3-12x2+36x-36       .......(1)By second derivative of equation (1), we get…

Q: 4х + 1 f(x) = 2 – 5x2

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Q: f"(x) = f(x) = (x + 6)(x − 6)(x +,5)(x – 5) X Solve the equation f'(x) = 0. (Enter your answers as a…

A: To find second derivative of

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 5. h(x) = 2-9, 3 x+5 %3D 6. A(x) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the second derivative of f (x) = 3e5x− 8e-6x

A: Given ,  f (x) = 3e5x-8e-6x we have to find the second derivative of the given function.

Q: y=x1.5+1/x2.5 find the derivative. I am getting a solution but I'm unsure of how it is x3.5 at the…

A: y=x1.5+1/x2.5

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.