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If h(x) = 2xsin(2x), find h'(x).

Differentiate using product rule as expression consist of two functions.Product Rule: d(f(x)g(x))/dx = g(x).f'(x) + f(x).g'(x)Chain Rule: d(f(g(x)))/dx = g'(x) . f'(g(x))
Let: f(x) = 2x f'(x) = 2 - s...

Answered by Meer S. • Maths tutor

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Differentiate the following: y = 3x^(1/3) + 2

Answer: dy/dx = x^-2/3Explanation: When differentiating, we bring the power to the front and subtract 1 from the power to get the new power. So the first term becomes (3 x 1/3)x^{(1/3 - 1)}

Answered by Scarlett S. • Maths tutor

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Find the intergral of 2x^5 - 1/4x^3 - 5 with respect to x.

2x⁵ - 1/4x³ - 5 can be intergrated by intergrating each term seperately and then remembering to add a constant to your new answer. Therefore the correct answer would be x⁶...

Answered by George H. • Maths tutor

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differentiate y=8x^3 - 4*x^(1/2) + (3x^2 + 2)/x

y= 24x^2 - 2x^(-1/2) + 3 - 2x^-2

Answered by Abubakar M. • Maths tutor

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Given a function f(x)=3x^2+5x-1, find its derivative.

Derivative of 3x^2 is 3*(derivative of x^2) which is 3*(2x)=6x. Derivative of 5x is 5*(Derivative of x) which is 5*1=5 and derivative of (-1) is 0. Hence the answer is derivative of f(x) defined above is ...

Answered by Carla F. • Maths tutor

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