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Evaluate the derivative of f(x) = 3x⁻¹⁰ + x⁵ - 5x² - x⁻¹ + 10 using the power rule.

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f'(x) = d(3x⁻¹⁰ + x⁵ - 5x² - x⁻¹ + 10)/dx

= 3d(x⁻¹⁰)/dx + d(x⁵)/dx - 5d(x²)/dx - d(x⁻¹)/dx + d(10)/dx

= f'(x) = -30x⁻¹¹ + 5x⁴ - 10x + x⁻²

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Use the product rule to find the following derivatives.

y = exsin(x)

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Let f(x) = ex and g(x) = sin(x), then apply the product rule:

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Is g(x)=ln(sin(x)) a composite function? If so, what are the "inner" and "outer" functions?

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Use the quotient rule to find the following derivatives.

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 Velocity, Acceleration, and Second Derivative

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 Velocity, Acceleration, and Second Derivative

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The position of a particle on a line is given by s(t) = t ³ − 3 t ² − 6 t + 5, where t is measured in seconds and s is measured in feet. Find

The velocity of the particle at the end of 2 seconds.