"Differentiate y2=4ax w.r.t x(Where a is a constant)?" was answered by students like you

High School
Calculus and Analysis
Calculus 1
Derivatives

Breanna Mcclure

Answered question

2022-04-12

Differentiate

y^{2} = 4 a x

w.r.t x(Where a is a constant)?

Answer & Explanation

tabuevniru8op

Beginner2022-04-13Added 14 answers

When we differentiate y wrt x we get

\frac{d y}{d x}

However, we only differentiate explicit functions of y wrt x. But if we apply the chain rule we can differentiate an implicit function of y wrt y but we must also multiply the result by

\frac{d y}{d x}

.
Example:

\frac{d}{d x} (y^{2}) = \frac{d}{d y} (y^{2}) \frac{d y}{d x} = 2 y \frac{d y}{d x}

When this is done in situ it is known as implicit differentiation.
Now, we have:

y^{2} = 4 a x

, the equation of a Parabola in standard form
Implicitly differentiating wrt x

\frac{d}{d x} y^{2} = \frac{d}{d x} 4 a x

∴ 2 y \frac{d y}{d x} = 4 a

∴ \frac{d y}{d x} = \frac{4 a}{2 y}

∴ \frac{d y}{d x} = \frac{2 a}{y}

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