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प्रश्न
Find `dy/dx`, if x = e3t, y = `e^((4t + 5))`
योग
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उत्तर
x = e3t
Differentiating both sides w.r.t. t, we get
`dx/dt = e^(3t) * (3) = 3 e^(3t)`
y = `e^(4t + 5)`
Differentiating both sides w.r.t. t, we get
`dy/dt = e^((4t + 5)) xx 4`
`= 4 * e^((4t + 5))`
∴ `dy/dx = ((dy/dt))/((dx/dt))`
= `(4 * e^(4t + 5))/(3* e^(3t))`
`= 4/3 e^(4t + 5 - 3t)`
`= 4/3 e^(t + 5)`
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