so say y = 2^x
dy/dx = ln2.2^x
(. = multiplication symbol, ^ = to-the-power-of symbol)
The general formula is
(where 'a' is a constant, x is what you are differentiating with respect to and y is f(x))
y = a^x
then
dy/dx = lna.a^x
Go ask a math teacher or look up exponential function differentiation on the internet for why.
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y = Sin(x) dy/dx = Cos(x)
You should apply the chain rule d/dx(x.sin x) = x * d/dx(sin x) + sin x * d/dx(x) = x * cos x + sin x * 1 = x.cos x + sin x
Assuming X and x are the same then x2 + x2 = 2x2.
y=x3+ 2x, dx/dt=5, x=2, dy/dt=? Differentiate the equation with respect to t. dy/dt=3x2*dx/dt Substitute in known values. dy/dt=3(2)2 * (5) dy/dt=60
The power law of indices says: (x^a)^b = x^(ab) = x^(ba) = (x^b)^a → e^(2x) = (e^x)² but e^x = 2 → e^(2x) = (e^x)² = 2² = 4