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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Differentiation

NDA 2013 · Mathematics · Differentiation

What is the derivative of x^3 with respect to x^2 ?

What is the derivative of x3x^3 with respect to x2x^2 ?

Options

  1. A3x23 x^2
  2. B3x2\frac{3 x}{2}
  3. Cxx
  4. D32\frac{3}{2}

Correct answer

B. 3x2\frac{3 x}{2}

Step-by-step solution

Let p=x3,q=x2p=x^3, q=x^2 Now, dpdx=3x2,dqdx=2x\frac{d p}{d x}=3 x^2, \frac{d q}{d x}=2 x derivative of pp w.r.t. qq is dpdq=dpdxdqdx=3x22x=32x\frac{d p}{d q}=\frac{\frac{d p}{d x}}{\frac{d q}{d x}}=\frac{3 x^2}{2 x}=\frac{3}{2} x
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