# How to differentiate these functions?

What are the derivatives of these functions?

5x^2cos(5x^2 +2)

8sin(2x^2)

These are (dP/dV)

P= ( (nRTsin(v)) / 2v ) + abn^2

P= (RTsin(v)+b) (1+an^2v)

P= (nRT)/(nsin(v)-a)

### 1 Answer

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- 1 decade agoFavorite Answer
d/dx [5x^2cos(5x^2 +2)] =10x cos(5x^2 +2) + 5x^2 (-1)sin (5x^2 +2) (10x)

= 10x cos(5x^2 +2) - 50x^3 sin (5x^2 +2)

d/dx [8sin(2x^2)] = 8 cos (2x^2) (4x) = 32 x cos (2x^2)

d/dV [ ( (nRTsin(V)) / 2v ) + abn^2] = [ nRT cos V (2V) - nRT sin V (2) / (2V)^2 ] + 0

=nRT[V cos V - sin V] / 2V^2

d/dV [(RTsin(V)+b) (1+an^2V)] = RT cos V (1 + an^2 V) + (RTsin V +b)an^2

d/dV [(nRT)/(nsin(V)-a) ] = nRT(-1)(n sin V -a)^{-2} (n cos V)

= -n^2 RT cos V /(n sin V -1)^2.

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