The derivative of f(x) is
lim h-->0 [f(x+h)-f(x)]/h.
So let f(x) = -5x. The derivative is
lim h-->0 [-5(x+h)- -5(x)]/h
= lim h-->0 [-5x - 5h + 5x]/h
= lim h-->0 -5h/h
Since the limit h-->0 of h/h is 1, the derivative is
-5
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You will find several formulae in the Wikipedia article on "derivative".
The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
To find the derivative of ( \frac{3}{\sqrt{x}} ), we can rewrite it as ( 3x^{-\frac{1}{2}} ). Using the power rule, the derivative is ( -\frac{3}{2} x^{-\frac{3}{2}} ). This can also be expressed as ( -\frac{3}{2\sqrt{x^3}} ).
2 x 2 = 4. 4 is a constant. The derivative of a constant is always 0. Therefore, The derivative of 2 x 2 is zero.
we have to find out dy/dx of sinx0 ----