What is the derivative of 5t^2ln(t) ?

The derivative of 5t^2ln(t) is 5(2tln(t)+t)

What is the first derivative of 5t^2ln(t) ?

The first derivative of 5t^2ln(t) is 5(2tln(t)+t)

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derivative of

5 t^{2} ln (t)

5 (2 t ln (t) + t)

Solution steps

\frac{d}{d t} (5 t^{2} ln (t))

Take the constant out:

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

= 5 \frac{d}{d t} (t^{2} ln (t))

Apply the Product Rule:

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

f = t^{2}, g = ln (t)

= 5 (\frac{d}{d t} (t^{2}) ln (t) + \frac{d}{d t} (ln (t)) t^{2})

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

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

= 5 (2 t ln (t) + \frac{1}{t} t^{2})

\frac{1}{t} t^{2} = t

= 5 (2 t ln (t) + t)

e^{x}, e^{- 4 x}, ln (3)

f (x) = 7 e^{x} + x

\int e \cdot t^{2} d t

x^{- 5} + x^{\frac{1}{2}}

\frac{\partial}{\partial x} (2 e^{x - y})

What is the derivative of 5t^2ln(t) ?
The derivative of 5t^2ln(t) is 5(2tln(t)+t)
What is the first derivative of 5t^2ln(t) ?
The first derivative of 5t^2ln(t) is 5(2tln(t)+t)