Differentiate the following w.r.t.x: from Mathematics Continu

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Continuity and Differentiability

Short Answer Type

181. Differentiate the following w.r.t.x:

square root of log space left parenthesis straight x cubed plus straight e to the power of straight x right parenthesis end root

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182. Differentiate the following w.r.t.x: $square root of log space left parenthesis logx right parenthesis end root$

Let space straight y equals square root of log space left parenthesis logx right parenthesis end root equals left square bracket log space left parenthesis logx right parenthesis right square bracket to the power of begin inline style 1 half end style end exponent therefore dy over dx equals 1 half left square bracket log space left parenthesis logx right parenthesis right square bracket to the power of negative begin inline style 1 half end style end exponent straight d over dx left square bracket log space left parenthesis logx right parenthesis right square bracket equals fraction numerator 1 over denominator 2 square root of log space left parenthesis logx right parenthesis end root end fraction cross times fraction numerator 1 over denominator log space straight x end fraction cross times straight d over dx left parenthesis log space straight x right parenthesis equals fraction numerator 1 over denominator 2 square root of log space left parenthesis logx right parenthesis end root end fraction cross times fraction numerator 1 over denominator log space straight x end fraction cross times 1 over straight x equals fraction numerator 1 over denominator 2 xlog space straight x square root of log space left parenthesis logx right parenthesis end root end fraction

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183. Differentiate the following w.r.t.x:

log open square brackets straight e to the power of 3 straight x end exponent open parentheses fraction numerator 5 straight x minus 3 over denominator 4 straight x plus 2 end fraction close parentheses to the power of 1 third end exponent close square brackets

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184. Differentiate the following w.r.t.x:

log open parentheses straight x plus 2 plus square root of straight x squared plus 4 straight x plus 1 end root close parentheses

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185. Differentiate the following w.r.t.x:

log open parentheses straight x plus square root of 1 plus straight x squared end root close parentheses

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186. Differentiate the following w.r.t.x:

log open parentheses square root of straight x minus straight a end root plus square root of straight x minus straight b end root close parentheses

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Long Answer Type

187. Differentiate the following w.r.t.x:

log open parentheses fraction numerator square root of straight a plus straight x end root plus square root of straight a minus straight x end root over denominator square root of straight a plus straight x end root minus square root of straight a minus straight x end root end fraction close parentheses

74 Views

Short Answer Type

188. Differentiate the following w.r.t.x:

open parentheses fraction numerator straight x plus square root of straight x squared minus straight a squared end root over denominator straight x minus square root of straight x squared minus straight a squared end root end fraction close parentheses

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189. Differentiate :

5 to the power of square root of straight x squared plus 1 end root end exponent plus open parentheses square root of straight x squared plus 1 end root close parentheses to the power of 5

w.r.t x.

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190. Differentiate :

straight x square root of straight x squared plus 1 end root plus log open parentheses square root of straight x squared plus 1 end root close parentheses

w.r.t x.

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