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Popular >

derivative of t^5ln|t|

Solution

derivative of

t^{5} ln ∣ t ∣

Solution

5 t^{4} ln ∣ t ∣ + t^{4}

Solution steps

\frac{d}{d t} (t^{5} ln ∣ t ∣)

Apply the Product Rule:

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

f = t^{5}, g = ln ∣ t ∣

= \frac{d}{d t} (t^{5}) ln ∣ t ∣ + \frac{d}{d t} (ln ∣ t ∣) t^{5}

\frac{d}{d t} (t^{5}) = 5 t^{4}

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

= 5 t^{4} ln ∣ t ∣ + \frac{1}{t} t^{5}

\frac{1}{t} t^{5} = t^{4}

= 5 t^{4} ln ∣ t ∣ + t^{4}

Popular Examples

(\partial)/(\partial x)(log_{10}(xy))

\frac{\partial}{\partial x} (lo g_{10} (x y))

area y=x^2-2x,y=-x^2+4x area

y = x^{2} - 2 x, y = - x^{2} + 4 x

limit as x approaches 2+of 3/(x^2-4)

x \to 2 + lim (\frac{3}{x ^{2} - 4})

sum from n=1 to infinity of 1/(n^4+1)

n = 1 \sum \infty \frac{1}{n ^{4} + 1}

derivative of sqrt(r)+\sqrt[5]{r}derivative of

Frequently Asked Questions (FAQ)

What is the derivative of t^5ln|t| ?
The derivative of t^5ln|t| is 5t^4ln|t|+t^4
What is the first derivative of t^5ln|t| ?
The first derivative of t^5ln|t| is 5t^4ln|t|+t^4