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LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES4 Marks
Question
Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{\text{ax+b}}{\text{cx+d}}$
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Answer

Let $\text{f(x)}=\frac{\text{ax+b}}{\text{cx+d}}$ By quotient rule, $\text{f}'\text{(x)}=\frac{\text{(cx+d)}\frac{\text{d}}{\text{dx}}\text{(ax+b)}-\text{(ax+b)}\frac{\text{d}}{\text{dx}}\text{(cx+d)}}{(\text{cx+d})^2}$ $=\frac{\text{(cx+d)(a)}-\text{(ax+b)}\text{(c)}}{\text{(cx+d)}^2}$ $=\frac{\text{acx+ad}-\text{acx+bc}}{\text{(cx+d})^2}$ $=\frac{\text{ad}-\text{bc}}{\text{(cx+d)}^2}$

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