What is the derivative of sqrt(35x)ln(10x) ?

The derivative of sqrt(35x)ln(10x) is (sqrt(35)ln(10x)}{2sqrt(x)}+sqrt(\frac{35)/x)

What is the first derivative of sqrt(35x)ln(10x) ?

The first derivative of sqrt(35x)ln(10x) is (sqrt(35)ln(10x)}{2sqrt(x)}+sqrt(\frac{35)/x)

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derivative of

35 x ln (10 x)

\frac{35 ln ( 10 x )}{2 x} + \frac{35}{x}

Solution steps

\frac{d}{d x} (35 x ln (10 x))

Apply the Product Rule:

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

f = 35 x, g = ln (10 x)

= \frac{d}{d x} (35 x) ln (10 x) + \frac{d}{d x} (ln (10 x)) 35 x

\frac{d}{d x} (35 x) = \frac{35}{2 x}

\frac{d}{d x} (ln (10 x)) = \frac{1}{x}

= \frac{35}{2 x} ln (10 x) + \frac{1}{x} 35 x

Simplify

\frac{35}{2 x} ln (10 x) + \frac{1}{x} 35 x : \frac{35 ln ( 10 x )}{2 x} + \frac{35}{x}

= \frac{35 ln ( 10 x )}{2 x} + \frac{35}{x}

(1 + x^{4}) d y + x (1 + 4 y^{2}) d x = 0, y (1) = 0

4 y^{^{''}} - y = 1

\int e^{3 x} d x

(x^{2} - 9)^{2}

y^{^{''}} - 3 y^{^{'}} - 10 y = 4, y (0) = 0, y^{^{'}} (0) = 0

What is the derivative of sqrt(35x)ln(10x) ?
The derivative of sqrt(35x)ln(10x) is (sqrt(35)ln(10x)}{2sqrt(x)}+sqrt(\frac{35)/x)
What is the first derivative of sqrt(35x)ln(10x) ?
The first derivative of sqrt(35x)ln(10x) is (sqrt(35)ln(10x)}{2sqrt(x)}+sqrt(\frac{35)/x)