If 1 6 5 4 3 2 5 4 3 2 y = x + x + x + x + x + find dx dy .
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Step-by-step explanation:
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Class 11
>>Applied Mathematics
>>Differentiation
>>Rules of differentiation
>>Derivative of ( x + 3 ) ^ 2 ( x + 4 ) ^
Question
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Derivative of (x+3)
2
(x+4)
3
(x+5)
4
w.r. to x is
Medium
Solution
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Correct option is B)
(x+3)
2
(x+4)
3
(x+5)
4
dx
d
[(x+3)
2
(x+4)
3
(x+5)
4
]
2(x+3)(x+4)
3
(x+5)
4
+3(x+3)
2
(x+4)
2
(x+5)
4
+4(x+3)
2
(x+4)
3
(x+5)
3
Using chain rule we solve the above expressing
dx
d
[P(x)Q(x)R(x)]=P
′
(x)Q(x)R(x)+P(x)Q
′
(x)R(x)+P(x)Q(x)R
′
(x)
Q simplifying
(x+3)(x+4)
2
(x+5)
3
[2(x+4)(x+5)+3(x+3)(x+5)+4(x+4)(x+3)]
=(x+3)(x+4)
2
(x+5)
3
[2x
2
+18x+40+3x
2
+24x+45+4x
2
+28x+48]
=(x+3)(x+4)
2
(x+5)
3
[9x
2
+70x+133].