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Find the derivative of tan (2x + 3)....

Find the derivative of tan `(2x + 3)`.

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To find the derivative of \( \tan(2x + 3) \), we will use the chain rule of differentiation. Here are the steps to solve the problem: ### Step 1: Identify the outer and inner functions The function can be expressed as: - Outer function: \( f(u) = \tan(u) \) - Inner function: \( u = 2x + 3 \) ### Step 2: Differentiate the outer function ...
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NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Show that the function f defined by f(x)=|1-x+x|, where x is any real...

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  2. Find the derivative of the function given b y f(x) = sin(x^2)dot

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  3. Find the derivative of tan (2x + 3).

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  4. Differentiate sin(cos(x^2)) with respect to x.

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  5. Find (dy)/(dx)if x-y =pi

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  6. Find (dy)/(dx), if y + siny = cosx

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  7. Find the derivative of f given by f(x)=sin^(-1)xassuming it exists.

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  8. Find the derivative of / given by f(x)=tan^(-1)xassuming it exists.

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  9. Find df/dx if f(x) = (sin x) ^ sin x for all o lt x lt pi .

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  10. Differentiate sin^2xw.r.t e^(cosx).

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  11. Differentiate the following w.r.t x.(i) sqrt(3x+2)+(1/(sqrt(2x^2 + 4))...

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  12. Find fprime(x)if f(x)=(sinx)^(sinx)for all 0ltxltpi

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  13. Verify Rolles theorem for the function y=x^2+2,a=-2and b = 2.

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  14. Verify the Mean Value Theorm for f(x)=x^2 in the interval [2,4].

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  15. If y=3e^(2x)+2e^(3x). Prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0.

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  16. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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  17. Find all the points of discontinuity of the function f defined byf(x)=...

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  18. Discuss the continuity of the function f defined by f(x)={(x+2,"if",x...

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  19. Discuss the continuity of the function f given by f(x)={x , ifxgeq0x^2...

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  20. Discuss the continuity of the function defined byf(x)={x+2, ifx<0-x+2,...

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