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Continuity and Differentiability

Short Answer Type

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

straight e to the power of straight x cubed end exponent

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

square root of straight e to the power of square root of straight x end exponent end root comma straight X greater than 0

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153. Differentiate e^x + e^x² +....+ e^x⁵. w.r.t.x.

Let space space space space space space space space straight y equals straight e to the power of straight x plus straight e to the power of straight x squared end exponent plus straight e to the power of straight x cubed end exponent plus straight e to the power of straight x to the power of 4 plus straight e to the power of straight x to the power of 5 therefore space dy over dx equals straight d over dx open parentheses straight e to the power of straight x plus straight e to the power of straight x squared end exponent plus straight e to the power of straight x cubed end exponent plus straight e to the power of straight x to the power of 4 plus straight e to the power of straight x to the power of 5 close parentheses space space space space space space space space space space space space space equals straight d over dx open parentheses straight e to the power of straight x close parentheses plus straight d over dx open parentheses straight e to the power of straight x squared end exponent close parentheses plus straight d over dx open parentheses straight e to the power of straight x cubed end exponent close parentheses plus straight d over dx open parentheses straight e to the power of straight x to the power of 4 close parentheses plus straight d over dx open parentheses straight e to the power of straight x to the power of 5 close parentheses space space space space space space space space space space space space space equals straight e to the power of straight x. straight d over dx left parenthesis straight x right parenthesis plus straight e to the power of straight x squared end exponent. straight d over dx left parenthesis straight x squared right parenthesis plus straight e to the power of straight x cubed end exponent. straight d over dx left parenthesis straight x cubed right parenthesis plus straight e to the power of straight x to the power of 4. straight d over dx left parenthesis straight x to the power of 4 right parenthesis plus straight e to the power of straight x to the power of 5 straight d over dx open parentheses straight x to the power of 5 close parentheses space space space space space space space space space space space space space equals straight e to the power of straight x.1 plus straight e to the power of straight x squared end exponent.2 straight x plus straight e to the power of straight x cubed end exponent.3 straight x squared plus straight e to the power of straight x to the power of 4.4 straight x cubed plus straight e to the power of straight x to the power of 5.5 straight x to the power of 4 space space space space space space space space space space space space space equals straight e to the power of straight x plus 2 straight x space straight e to the power of straight x squared end exponent plus 3 straight x squared straight e to the power of straight x cubed end exponent plus 4 straight x cubed straight e to the power of straight x to the power of 4 plus 5 straight x to the power of 4 straight e to the power of straight x to the power of 5

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154. Differentiate the following w.r.t.x :log (log x),x>1

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155. Differentiate the following w.r.t.x :log7 (log x)

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156. Differentiate (3x² - 9 x + 5)⁹ w.r.t.x.

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157. Differentiate

square root of 15 straight x squared minus straight x plus 1 end root straight w. straight r. straight t space straight x

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158.

Differentiate space square root of 3 straight x plus 2 end root plus fraction numerator 1 over denominator square root of 2 straight x squared plus 4 end root end fraction straight w. straight r. straight t space space straight x.

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159. Differentiate

square root of fraction numerator straight x minus 1 over denominator straight x plus 2 end fraction end root

W.r.t x.

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

left parenthesis 4 straight x cubed minus 5 straight x squared plus 1 right parenthesis to the power of 4

91 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

153. Differentiate ex + ex2 +....+ ex5. w.r.t.x.

153. Differentiate e^x + e^x² +....+ e^x⁵. w.r.t.x.