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    Evaluating the gradient of a function

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    Find the gradient of the function: (3√θ^3) / 2sin2θ

    I have a number of these questions to complete could you please explain each step involved to get the correct answer

    © BrainMass Inc. brainmass.com December 24, 2021, 5:03 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/evaluating-gradient-function-24348

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    Find the gradient of the function: (3√θ^3) / 2sin2θ

    The gradient is a first-order differential operator that maps functions to vector fields. It is a generalization of the ordinary derivative.

    Here we have a function of θ. The gradient is found by differentiating this with respect to θ

    grad ((3√θ^3) / 2sin2θ) = d/d θ of [(3θ3/2) / 2sin2θ]

    Use the product rule or quotient rule here.

    Product rule:
    = (3θ3/2) * derivative of (1/2sin2θ) + (1/2sin2θ) * derivative of (3θ3/2)

    = (3θ3/2) * derivative of (1/2sin2θ) + (1/2sin2θ) * 3* 3/2 * θ3/2 -1)

    = (3θ3/2) * derivative of (1/2sin2θ) + (9 θ1/2/4sin2θ)

    = (3θ3/2) * (1/2) *derivative of cosec(2θ) + (9 θ1/2/4sin2θ)

    = (3θ3/2) * (1/2) * [-2 Cot(2θ) * Cosec (2θ)] + (9 θ1/2/4sin2θ)

    = - (3θ3/2) * Cot(2θ) * Cosec (2θ) + (9 θ1/2/4sin2θ)

    = - (3θ3/2) * Cot(2θ) * Cosec (2θ) + (9/4) Cosec2θ * θ1/2

    = (9/4) Cosec2θ * θ1/2 - (3θ3/2) * Cot(2θ) * Cosec (2θ)

    = [(9/4) θ1/2 - (3θ3/2) * Cot(2θ)] * Cosec (2θ) ---Answer

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:03 pm ad1c9bdddf>
    https://brainmass.com/math/derivatives/evaluating-gradient-function-24348

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