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Popular >

derivative of t^{11}ln|t|

Solution

derivative of

t^{11} ln ∣ t ∣

Solution

11 t^{10} ln ∣ t ∣ + t^{10}

Solution steps

\frac{d}{d t} (t^{11} ln ∣ t ∣)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{11}, g = ln ∣ t ∣

= \frac{d}{d t} (t^{11}) ln ∣ t ∣ + \frac{d}{d t} (ln ∣ t ∣) t^{11}

\frac{d}{d t} (t^{11}) = 11 t^{10}

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

= 11 t^{10} ln ∣ t ∣ + \frac{1}{t} t^{11}

\frac{1}{t} t^{11} = t^{10}

= 11 t^{10} ln ∣ t ∣ + t^{10}

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Frequently Asked Questions (FAQ)

What is the derivative of t^{11}ln|t| ?
The derivative of t^{11}ln|t| is 11t^{10}ln|t|+t^{10}
What is the first derivative of t^{11}ln|t| ?
The first derivative of t^{11}ln|t| is 11t^{10}ln|t|+t^{10}