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Differentiation (p-1) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Differentiation (p-1)2 Marks
Question
Differentiate the following w.r.t. x. : $x^{\frac{5}{2}}+5 x^{\frac{7}{5}}$
✓

Answer

$
x^{\frac{5}{2}}+5 x^{\frac{7}{5}}
$
Solution:
Let $\mathrm{y}=x^{\frac{5}{2}}+5 x^{\frac{7}{5}}$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x}\left(\begin{array}{c}
x^{\frac{5}{2}}+5 x^{\frac{7}{5}}
\end{array}\right) \\
& =\frac{\mathrm{d}}{\mathrm{d} x} x^{\frac{5}{2}}+5 \frac{\mathrm{d}}{\mathrm{d} x} x^{\frac{7}{5}} \\
& =\frac{5}{2} x^{\frac{5}{2}-1}+5 \frac{7}{5} x^{\frac{7}{5}-1} \\
& =\frac{5}{2} x^{\frac{3}{2}}+7 x^{\frac{2}{5}}
\end{aligned}
$

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