Derivative rules Flashcards
Derivative of:
Cos 𝓧
-sin 𝓧
Derivative of:
Tan 𝓧
Sec^2 𝓧
Derivative of:
Cot 𝓧
-csc^2 𝓧
Derivative of:
Sec 𝓧
Sec 𝓧 tan 𝓧
Derivative of:
Sin 𝓧
cos𝓧
Derivative of:
Csc 𝓧
-csc 𝓧 cot 𝓧
Constant Rule
f(x)= K
F(x)= 0
~Any constant
Power Rule
f(x)= X^n
f’(x)= nX^(n-1)
Constant Multiple Rule
f(x)=Ku
f’(x)=K(u’(x))
Sum Rule
f(x)=u(x)+v(x)
f’(x)=u’(x)+v’(x)
Difference Rule
f(x)=U(x)-V(x)
f’(x)=U’(x)-V’(x)
Exponential Function
f(x)=b^x
f’(x)= (Inb)b^x
Natural Exponential function
f(x)=e^x
f’(x)=e^x
Logarithmic Fuction
f(x)=logb(x)
f’(x)=1/(Inb)x
Natural log
f(x)=In(x)
f’(x)=1/x
Product Rule
f(x)=UV
f’(x)=U’V+UV’
Quotient Rule
f(x)=u/v
f’(x)=u’v-uv’/[v]^2
Chain Rule
f’(g(x)) • g’(x)
Sin ^-1(x)
[ arcSin(x)]
1/√1-x^2
Cos^-1(x)
[arcCos(x)]
-1/√1-x^2
tan^-1(x)
[arcTan(x)]
1/1+x^2
Cot^-1(x)
[arcCot(x)]
-1/1+x^2
Sec^-1(x)
[arcSec(x)]
1/|x| √x^2-1
Csc^-1(x)
[arcCsc(x)]
-1/|x| √x^2-1
Log(x)
Log10(x)
Inverse equation
1/f’h(x)
ln(A^R)
RIn(A)
In(A•B)
ln(A)+ln(B)
ln(A/B)
ln(A)-ln(B)
Epsilon Delta number line
X not - delta 1
X not
X not + delta 2
