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Popular >

derivative of 1/3 (3-5x^3)

Solution

\frac{d}{d x} (\frac{1}{3} (3 - 5 x)^{3})

Solution

- 5 (3 - 5 x)^{2}

Solution steps

\frac{d}{d x} (\frac{1}{3} (3 - 5 x)^{3})

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} ((3 - 5 x)^{3})

Apply the chain rule:

3 (3 - 5 x)^{2} \frac{d}{d x} (3 - 5 x)

= 3 (3 - 5 x)^{2} \frac{d}{d x} (3 - 5 x)

\frac{d}{d x} (3 - 5 x) = - 5

= \frac{1}{3} \cdot 3 (3 - 5 x)^{2} (- 5)

Simplify

\frac{1}{3} \cdot 3 (3 - 5 x)^{2} (- 5) : - 5 (3 - 5 x)^{2}

= - 5 (3 - 5 x)^{2}

Popular Examples

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\int_{0}^{2} \frac{16}{21 x ^{2}} d x

tangent of 9x^2,\at x=2 tangent of

9 x^{2}, at x = 2

integral of x/(x^2-x+6)

\int \frac{x}{x ^{2} - x + 6} d x

(\partial)/(\partial x)(a/(x^2))

\frac{\partial}{\partial x} (\frac{a}{x ^{2}})

(\partial)/(\partial x)(ln(x^6y))

\frac{\partial}{\partial x} (ln (x^{6} y))

Frequently Asked Questions (FAQ)

What is the derivative of 1/3 (3-5x^3) ?
The derivative of 1/3 (3-5x^3) is -5(3-5x)^2
What is the first derivative of 1/3 (3-5x^3) ?
The first derivative of 1/3 (3-5x^3) is -5(3-5x)^2