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Level 558

Derivatives


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Chain Rule:
dy/dx = (dy/dt)(dt/dx)
Product Rule:
dy/dx = u(dv/dx)+v(du/dx)
Quotient Rule:
dy/dx = (g(x)f'(x)-g'(x)f(x))/(g(x))^2
d(xⁿ)
nxⁿ⁻¹
d(cf(x))
c*f'(x)
d(f(x) + g(x))
f'(x) + g'(x)
d(c)
0
d(e^x)
e^x
d(a^x)
(lna)(a^x)
d(lnx)
1/x
d(logax)
1/((lna)x)
d(sinx)
cosx
d(cosx)
-sinx
d(tanx)
sec²x
d(cotx)
-csc²x
d(secx)
sexctanx
d(cscx)
-cscxcotx
d(f(g(x))
f'(g(x)) * g'(x)
d(f(x) * g(x))
f'(x)*g(x) + g'(x)*f(x)
d(f(x)/g(x))
(f'(x)*g(x) - g'(x)*f(x))/ (g(x))²
d(sin⁻¹(x))
1/√(1-x²)
d(cos⁻¹(x))
-1/√(1-x²)
d(tan⁻¹(x))
1/(1+x²)
d(cot⁻¹(x))
-1/(1+x²)
d(sec⁻¹(x))
1/|x|√(x²-1)
d(csc⁻¹(x))
-1/|x|√(x²-1)