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Popular >

derivative of x^6ln(7x)

Solution

\frac{d}{d x} (x^{6} ln (7 x))

Solution

6 x^{5} ln (7 x) + x^{5}

Solution steps

\frac{d}{d x} (x^{6} ln (7 x))

Apply the Product Rule:

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

f = x^{6}, g = ln (7 x)

= \frac{d}{d x} (x^{6}) ln (7 x) + \frac{d}{d x} (ln (7 x)) x^{6}

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

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

= 6 x^{5} ln (7 x) + \frac{1}{x} x^{6}

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

= 6 x^{5} ln (7 x) + x^{5}

Popular Examples

derivative of y= 1/((x^2-1)(x^2+3x+3))derivative of

y = \frac{1}{( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 )}

derivative of x^{9/4}

\frac{d}{d x} (x^{\frac{9}{4}})

derivative of f(θ)=sqrt(11θ)derivative of

f (θ) = 11 θ

f(s)=sqrt((s^2+1)/(s^2+4))

f (s) = \frac{s ^{2} + 1}{s ^{2} + 4}

integral from 1 to 4 of x-(x-2)^2

\int_{1}^{4} x - (x - 2)^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^6ln(7x) ?
The derivative of x^6ln(7x) is 6x^5ln(7x)+x^5
What is the first derivative of x^6ln(7x) ?
The first derivative of x^6ln(7x) is 6x^5ln(7x)+x^5