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CBSE Class 12-science Answered

Q- 4(vii) find second order derivative.
question image
Asked by majethiyarishat9566.12sdatl | 10 Jun, 2020, 11:22: AM
answered-by-expert Expert Answer
 
 
To find the second order derivative of y=tan(x+y)
Since y=tan(x+y)
tan-1y = x+y
Differentiating w.r.t x we have
 open parentheses fraction numerator 1 over denominator 1 plus y squared end fraction close parentheses space fraction numerator d y over denominator d x end fraction equals 1 plus fraction numerator d y over denominator d x end fraction rightwards double arrow open parentheses fraction numerator 1 over denominator 1 plus y squared end fraction minus 1 close parentheses fraction numerator d y over denominator d x end fraction equals 1 rightwards double arrow fraction numerator d y over denominator d x end fraction equals negative fraction numerator 1 plus y squared over denominator y squared end fraction A g a i n space d i f f e r e n t i a t i n g space w. r. t space x comma space w e space g e t fraction numerator d squared y over denominator d x squared end fraction equals negative fraction numerator y squared open parentheses 2 y close parentheses begin display style fraction numerator d y over denominator d x end fraction end style minus open parentheses 1 plus y squared close parentheses open parentheses 2 y close parentheses begin display style fraction numerator d y over denominator d x end fraction end style over denominator y to the power of 4 end fraction equals fraction numerator negative open parentheses 2 y close parentheses begin display style fraction numerator d y over denominator d x end fraction end style open square brackets y squared minus 1 minus y squared close square brackets over denominator y to the power of 4 end fraction equals 2 over y cubed fraction numerator d y over denominator d x end fraction equals 2 over y cubed open parentheses negative fraction numerator 1 plus y squared over denominator y squared end fraction close parentheses equals negative fraction numerator 2 open parentheses 1 plus y squared close parentheses over denominator y to the power of 5 end fraction
Answered by Renu Varma | 10 Jun, 2020, 01:22: PM

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