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Differentiation: How to relate questions to steps to solve? - Coggle…
Differentiation: How to relate questions to steps to solve?
chain rule
y=(14x-2x³)³
steps:
differentiate the 'outside' power
multiply power to the front
power minus 1: 3(14x-2x³)^(3-1)
then differentiate the 'inside' bracket: (14-6x²)
multiply these two expressions together: 3(14x-2x³)²x(14-6x²)
6. simplify it until simplest form: dy/dx=3(14-6x²)(14x-2x³)²
power rule
y=4x²+17x
steps:
multiply power to the front: 2(4x)+17
2. power minus 1: dy/dx=8x+17
exponential function
y=e^(3x-7)
steps:
identify the e: y=
e
^(3x-7)
differentiate the power: d/dx(3x-7)=3
3. multiply power to the front: dy/dx=3e^(3x-7)