Use Implicit Differentiation to Find Dy/dx $\cos x y + x ^ { 5 } = y ^ { 5 }$

question 121

Multiple Choice

Use implicit differentiation to find dy/dx.
- $\cos x y + x ^ { 5 } = y ^ { 5 }$

• A) \(\frac { 5 x ^ { 4 } - x \sin x y } { 5 y ^ { 4 } }\)
• B) \(\frac { 5 x ^ { 4 } + x \sin x y } { 5 y ^ { 4 } }\)
• C) \(\frac { 5 x ^ { 4 } + y \sin x y } { 5 y ^ { 4 } - x \sin x y }\)
• D) \(\frac { 5 x ^ { 4 } - y \sin x y } { 5 y ^ { 4 } + x \sin x y }\)

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Definitions:

Neuromodulator

A substance released by neurons that adjusts the activity of other neurons or synapses, modulating the overall behavior of the brain and body.

Neurotransmitters

Chemical substances produced by neurons that transmit signals across a chemical synapse from one neuron to another target neuron, muscle cell, or gland cell.

Presynaptic Facilitation

An increase in the neurotransmitter release from a presynaptic neuron, enhancing the response of the postsynaptic neuron.

Myelinated Fiber

A nerve fiber with a myelin sheath, which increases the speed at which electrical impulses propagate along the nerve fiber.