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Popular >

derivative of y=5x^7ln(x)

Solution

derivative of

y = 5 x^{7} ln (x)

Solution

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

Solution steps

\frac{d}{d x} (5 x^{7} ln (x))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{7} ln (x))

Apply the Product Rule:

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

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

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

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

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

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

\frac{1}{x} x^{7} = x^{6}

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

Popular Examples

derivative of e^x-x^2+3x-2

\frac{d}{d x} (e^{x} - x^{2} + 3 x - 2)

integral from-2 to 3 of (17)/(x^4)

\int_{- 2}^{3} \frac{17}{x ^{4}} d x

y^{^{''}} = 2 y^{^{'}} + 8 y

integral of 4/3 e^{4x}

\int \frac{4}{3} e^{4 x} d x

derivative of (x^2+3^3)

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

Frequently Asked Questions (FAQ)

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