What is the derivative of 4xlog_{10}(x^9) ?

The derivative of 4xlog_{10}(x^9) is 4(log_{10}(x^9)+9/(ln(10)))

What is the first derivative of 4xlog_{10}(x^9) ?

The first derivative of 4xlog_{10}(x^9) is 4(log_{10}(x^9)+9/(ln(10)))

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derivative of

4 x lo g_{10} (x^{9})

4 (lo g_{10} (x^{9}) + \frac{9}{ln ( 10 )})

Solution steps

\frac{d}{d x} (4 x lo g_{10} (x^{9}))

Take the constant out:

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

= 4 \frac{d}{d x} (x lo g_{10} (x^{9}))

Apply the Product Rule:

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

f = x, g = lo g_{10} (x^{9})

= 4 (\frac{d x}{d x} lo g_{10} (x^{9}) + \frac{d}{d x} (lo g_{10} (x^{9})) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (lo g_{10} (x^{9})) = \frac{9}{ln ( 10 ) x}

= 4 (1 \cdot lo g_{10} (x^{9}) + \frac{9}{ln ( 10 ) x} x)

Simplify

4 (1 \cdot lo g_{10} (x^{9}) + \frac{9}{ln ( 10 ) x} x) : 4 (lo g_{10} (x^{9}) + \frac{9}{ln ( 10 )})

= 4 (lo g_{10} (x^{9}) + \frac{9}{ln ( 10 )})

\int \frac{5 x ^{7} - 9 x ^{5}}{x ^{3}} d x

f (x) = \frac{2 x}{2 + x}

\frac{\partial}{\partial x} (4 x cos (y))

5 sin (4 t)

\frac{\partial}{\partial z} (x^{y})

What is the derivative of 4xlog_{10}(x^9) ?
The derivative of 4xlog_{10}(x^9) is 4(log_{10}(x^9)+9/(ln(10)))
What is the first derivative of 4xlog_{10}(x^9) ?
The first derivative of 4xlog_{10}(x^9) is 4(log_{10}(x^9)+9/(ln(10)))