What is the derivative of y=5x^6ln(x) ?

The derivative of y=5x^6ln(x) is 5(6x^5ln(x)+x^5)

What is the first derivative of y=5x^6ln(x) ?

The first derivative of y=5x^6ln(x) is 5(6x^5ln(x)+x^5)

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derivative of

y = 5 x^{6} ln (x)

5 (6 x^{5} ln (x) + x^{5})

Solution steps

\frac{d}{d x} (5 x^{6} ln (x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{6} ln (x))

Apply the Product Rule:

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

f = x^{6}, g = ln (x)

= 5 (\frac{d}{d x} (x^{6}) ln (x) + \frac{d}{d x} (ln (x)) x^{6})

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 5 (6 x^{5} ln (x) + \frac{1}{x} x^{6})

\frac{1}{x} x^{6} = x^{5}

= 5 (6 x^{5} ln (x) + x^{5})

x \to 0 lim (\frac{1}{cos ( x ) - 1})

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

\int \frac{8 t - 5}{t + 1} d t

\int 24 x^{3} d x

What is the derivative of y=5x^6ln(x) ?
The derivative of y=5x^6ln(x) is 5(6x^5ln(x)+x^5)
What is the first derivative of y=5x^6ln(x) ?
The first derivative of y=5x^6ln(x) is 5(6x^5ln(x)+x^5)