What is the derivative of x^3ln(7x) ?

The derivative of x^3ln(7x) is 3x^2ln(7x)+x^2

What is the first derivative of x^3ln(7x) ?

The first derivative of x^3ln(7x) is 3x^2ln(7x)+x^2

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\frac{d}{d x} (x^{3} ln (7 x))

3 x^{2} ln (7 x) + x^{2}

Solution steps

\frac{d}{d x} (x^{3} ln (7 x))

Apply the Product Rule:

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

f = x^{3}, g = ln (7 x)

= \frac{d}{d x} (x^{3}) ln (7 x) + \frac{d}{d x} (ln (7 x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (ln (7 x)) = \frac{1}{x}

= 3 x^{2} ln (7 x) + \frac{1}{x} x^{3}

\frac{1}{x} x^{3} = x^{2}

= 3 x^{2} ln (7 x) + x^{2}

f (x) = e^{4 - 5 x} (3 x^{3} - 2)^{6}

y^{^{'}} = 2 x + y, y (0) = 9

y^{^{''}} - y = 10 sin^{2} (x)

\int 2^{x} (2^{- x} + 1) d x

\int \frac{1}{x ^{2} + 100} d x

What is the derivative of x^3ln(7x) ?
The derivative of x^3ln(7x) is 3x^2ln(7x)+x^2
What is the first derivative of x^3ln(7x) ?
The first derivative of x^3ln(7x) is 3x^2ln(7x)+x^2