Partial derivative formula:

1.y=c(c is a constant) y'=0

2.y=x^n y'=nx^(n- 1)

3.y=a^x； y'=a^xlna； y=e^x y'=e^x

4 . y = logax y ' = logae/x； y=lnx y'= 1/x

5.y=sinx y'=cosx

Derivative proof:

y=a^x

Take the logarithm of both sides at the same time and get: lny=xlna.

Derive x on both sides at the same time and get: y'/y=lna.

So y' = ylna = a xlna proves this point.

Matters needing attention

1. Not all functions can be exported;

2. The derivable function must be continuous, but the continuous function is not necessarily derivable (for example, y=|x| is not derivable at y=0).

When exporting extended data, you need to use several common formulas:

1. Chain rule: y=f[g(x)]

2.y=u*v, y'=u'v+uv' (generalized Leibniz formula)

3.y=u/v，y' = (u' v-uv')/v 2。 In fact, 4 can be directly derived from 3.

4. Derivation rule of inverse function: If the inverse function of y=f(x) is x=g(y), then there is y'= 1/x'