What is the derivative of t^x ?

The derivative of t^x is t^xln(t)

What is the first derivative of t^x ?

The first derivative of t^x is t^xln(t)

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\frac{d}{d x} (t^{x})

t^{x} ln (t)

Solution steps

\frac{d}{d x} (t^{x})

Treat

t

as a constant

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= t^{x} ln (t)

\frac{d}{d x} (sec (\frac{π}{3}))

(x + 2)^{2} y^{^{'}} + 5 (x + 2) y = 16, y (0) = 4

\int 5 x^{- 7} d x

x^{3} y^{2} = x y^{3} + 6, (2, 1)

\frac{d}{d x} (lo g_{5} (6 x^{3}))