What is the derivative of f(x)=2^xln(2) ?

The derivative of f(x)=2^xln(2) is ln^2(2)*2^x

What is the first derivative of f(x)=2^xln(2) ?

The first derivative of f(x)=2^xln(2) is ln^2(2)*2^x

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derivative of

f (x) = 2^{x} ln (2)

ln^{2} (2) \cdot 2^{x}

Solution steps

\frac{d}{d x} (2^{x} ln (2))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (2) \frac{d}{d x} (2^{x})

Apply the derivative exponent rule:

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

= ln (2) \cdot 2^{x} ln (2)

Simplify

ln (2) \cdot 2^{x} ln (2) : ln^{2} (2) \cdot 2^{x}

= ln^{2} (2) \cdot 2^{x}

y^{^{'}} = y + x^{2}

\frac{d y}{d x} = \frac{x ( e ^{x^{2}} + 2 )}{6 y ^{2}}

y = (6 x - 2) (5 x + 7)

\int_{0}^{4 π} t^{2} sin (2 t) d t

What is the derivative of f(x)=2^xln(2) ?
The derivative of f(x)=2^xln(2) is ln^2(2)*2^x
What is the first derivative of f(x)=2^xln(2) ?
The first derivative of f(x)=2^xln(2) is ln^2(2)*2^x