What is the derivative of 370*2^{(1/10 x)} ?

The derivative of 370*2^{(1/10 x)} is 37ln(2)*2^{x/(10)}

What is the first derivative of 370*2^{(1/10 x)} ?

The first derivative of 370*2^{(1/10 x)} is 37ln(2)*2^{x/(10)}

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derivative of

370 \cdot 2^{(\frac{1}{10} x)}

37 ln (2) \cdot 2^{\frac{x}{10}}

Solution steps

\frac{d}{d x} (370 \cdot 2^{\frac{1}{10} x})

Simplify

370 \cdot 2^{\frac{1}{10} x} : 185 \cdot 2^{1 + \frac{x}{10}}

= \frac{d}{d x} (185 \cdot 2^{1 + \frac{x}{10}})

Take the constant out:

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

= 185 \frac{d}{d x} (2^{1 + \frac{x}{10}})

Apply exponent rule:

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

2^{1 + \frac{x}{10}} = e^{(1 + \frac{x}{10}) l n (2)}

= 185 \frac{d}{d x} (e^{(1 + \frac{x}{10}) l n (2)})

Apply the chain rule:

e^{(1 + \frac{x}{10}) l n (2)} \frac{d}{d x} ((1 + \frac{x}{10}) ln (2))

= e^{(1 + \frac{x}{10}) l n (2)} \frac{d}{d x} ((1 + \frac{x}{10}) ln (2))

\frac{d}{d x} ((1 + \frac{x}{10}) ln (2)) = \frac{1}{10} ln (2)

= 185 e^{(1 + \frac{x}{10}) l n (2)} \frac{1}{10} ln (2)

Simplify

185 e^{(1 + \frac{x}{10}) l n (2)} \frac{1}{10} ln (2) : 37 ln (2) \cdot 2^{\frac{x}{10}}

= 37 ln (2) \cdot 2^{\frac{x}{10}}

What is the derivative of 370*2^{(1/10 x)} ?
The derivative of 370*2^{(1/10 x)} is 37ln(2)*2^{x/(10)}
What is the first derivative of 370*2^{(1/10 x)} ?
The first derivative of 370*2^{(1/10 x)} is 37ln(2)*2^{x/(10)}