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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives3 Marks
Question
Differentiate the following functions.
$(2\text{x}-7)^{2}(3\text{x}+5)^{3}$
✓

Answer

$\frac{\text{d}}{\text{dx}}(2\text{x}-7)^{2}(3\text{x}+5)^{3}$
$=(2\text{x}-7^{2}).\frac{\text{d}}{\text{dx}}(3\text{x}+5)^{3}+(3\text{x}+5)^{3}.\frac{\text{d}}{\text{dx}}(2\text{x}-7)^{2}$
$[$Using product Rule$]$
$\Rightarrow (2x - 7)^2.3(3x + 5)^2.3 + (3x + 5)^3.2(2x - 7).2$
$\Rightarrow 9(2x - 7)^2(3x + 5)^2[9(2x) - 7) + 4(3x + 5)]$
$\Rightarrow (2x - 7)(3x - 5)^2(18 - 63 + 12x + 20)$
$\Rightarrow (2x - 7)(3x + 5)^2(30x - 43)$
Hence, the required answer is $(2x - 7)(30x - 43)(3x + 5)^2.$

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