What is the d/(dt)(10^{2sqrt(t)}) ?

The d/(dt)(10^{2sqrt(t)}) is (ln(10)*100^{sqrt(t)})/(sqrt(t))

What is the first d/(dt)(10^{2sqrt(t)}) ?

The first d/(dt)(10^{2sqrt(t)}) is (ln(10)*100^{sqrt(t)})/(sqrt(t))

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\frac{d}{d t} (1 0^{2 t})

\frac{ln ( 10 ) \cdot 10 0 ^{t}}{t}

Solution steps

\frac{d}{d t} (1 0^{2 t})

Simplify

1 0^{2 t} : 10 0^{t}

= \frac{d}{d t} (10 0^{t})

Apply exponent rule:

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

10 0^{t} = e^{t l n (100)}

= \frac{d}{d t} (e^{t l n (100)})

Apply the chain rule:

e^{t l n (100)} \frac{d}{d t} (t ln (100))

= e^{t l n (100)} \frac{d}{d t} (t ln (100))

\frac{d}{d t} (t ln (100)) = \frac{ln ( 10 )}{t}

= e^{t l n (100)} \frac{ln ( 10 )}{t}

Simplify

e^{t l n (100)} \frac{ln ( 10 )}{t} : \frac{ln ( 10 ) \cdot 10 0 ^{t}}{t}

= \frac{ln ( 10 ) \cdot 10 0 ^{t}}{t}

\frac{d}{d x} (3^{t} (5 t^{4} + 7 t + y (t, x) (t, x)^{4}))

y = x^{\frac{2}{5}} (x + 3)

\int \frac{sin ( 7 x )}{1 + cos ^{2} ( 7 x )} d x

\frac{d}{d x} (\frac{x ^{3} - 4}{x - 1})

\frac{d y}{d x} = \frac{ln ( x )}{x y}, y (1) = 2

What is the d/(dt)(10^{2sqrt(t)}) ?
The d/(dt)(10^{2sqrt(t)}) is (ln(10)*100^{sqrt(t)})/(sqrt(t))
What is the first d/(dt)(10^{2sqrt(t)}) ?
The first d/(dt)(10^{2sqrt(t)}) is (ln(10)*100^{sqrt(t)})/(sqrt(t))