What is the derivative of g(t)=sqrt(2)^t ?

The derivative of g(t)=sqrt(2)^t is 1/2 ln(2)e^{(ln(2)t)/2}

What is the first derivative of g(t)=sqrt(2)^t ?

The first derivative of g(t)=sqrt(2)^t is 1/2 ln(2)e^{(ln(2)t)/2}

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derivative of

g (t) = 2^{t}

\frac{1}{2} ln (2) e^{\frac{l n ( 2 ) t}{2}}

Solution steps

\frac{d}{d t} ((2)^{t})

Simplify

(2)^{t} : 2^{\frac{t}{2}}

= \frac{d}{d t} (2^{\frac{t}{2}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{\frac{t}{2}} = e^{\frac{t}{2} l n (2)}

= \frac{d}{d t} (e^{\frac{t}{2} l n (2)})

Apply the chain rule:

e^{\frac{t}{2} l n (2)} \frac{d}{d t} (\frac{t}{2} ln (2))

= e^{\frac{t}{2} l n (2)} \frac{d}{d t} (\frac{t}{2} ln (2))

\frac{d}{d t} (\frac{t}{2} ln (2)) = \frac{1}{2} ln (2)

= e^{\frac{t}{2} l n (2)} \frac{1}{2} ln (2)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1}{2} ln (2) e^{\frac{l n ( 2 ) t}{2}}

x^{2} e^{x - 1}, at 1

\int cot (19 x) d x

\int x^{2} (3 x^{3} - 2)^{4} d x

\frac{d}{d x} (k^{x} + x^{k})

\int_{0}^{2} 2 π (x + 1) (12 - 6 x) d x

What is the derivative of g(t)=sqrt(2)^t ?
The derivative of g(t)=sqrt(2)^t is 1/2 ln(2)e^{(ln(2)t)/2}
What is the first derivative of g(t)=sqrt(2)^t ?
The first derivative of g(t)=sqrt(2)^t is 1/2 ln(2)e^{(ln(2)t)/2}