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Differentiate each of the following from...

Differentiate each of the following from first principle: `sqrt(sin(3x+1))`

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`f(x)=sqrt(sin(3x+1))`

`f'(x)=lim_(h->0)((f(x+h)-f(x))/(h)`

`f'(x)=lim_(h->0)(sqrt(sin(3x+3h+1))-sqrt(sin(3x+1)))/(h)`

`f'(x)=lim_(h->0)((sin(3x+3h+1))-(sin(3x+1)))/(h(sqrt(sin(3x+3h+1))+sqrt(sin(3x+1)))`

`f'(x)=lim_(h->0) (2cos((6x+3h+2)/(2))sin((3h)/(2)))/(h(sqrt(sin(3x+3h+1))+sqrt(sin(3x+1)))`

`f'(x)=lim_(h->0) (2cos((6x+3h+2)/(2))lim_(h->0) sin((3h)/(2))/(3h/2*2/3))*lim_(h->0) (1)/(sqrt(sin(3x+3h+1))+sqrt(sin(3x+1)))`

`f'(x)=(3cos (3x+1))/(2sqrt(sin(3x+1)))`

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RD SHARMA-DERIVATIVES-Solved Examples And Exercises
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  2. Differentiate each of the following from first principle: (sin x)/x

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  3. Differentiate each of the following from first principle: sqrt(sin(3x+...

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  4. Differentiate each of the following from first principle: e^(x^2+1)

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  6. Differentiate each of the following from first principle: tan(2x+1)

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  7. Differentiate each of the following from first principle: cossqrt(x)

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  8. Differentiate the following from first principle: tan2x

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  9. Differentiate each of the following from first principle: tansqrt(x)

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  10. Differentiate each of the following from first principle: (cos x)/x

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  11. Differentiate each of the following from first principle: sinx+cos x

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  12. Differentiate each of the following from first principle: e^(sqrt(2x))

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  13. Differentiate the following from first principle: 3^(x^2).

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  14. Differentiate each of the following from first principle: sqrt(tanx)

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  16. Differentiate the following with respect of x : (x^2-3x+2)(x+1)

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  17. Differentiate the following with respect of x :(sqrtx+1/(sqrtx))^3""

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  18. Differentiate the following with respect of x :(sin(x+a))/(cos x)

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  19. Differentiate the following with respect of x : x^4-2sinx+3cosx

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  20. Differentiate the following with respect of x :3^x+x^3+3^3

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