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Popular >

derivative of f(x)=ln(x^3+5x+3)

Solution

derivative of

f (x) = ln (x^{3} + 5 x + 3)

Solution

\frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

Solution steps

\frac{d}{d x} (ln (x^{3} + 5 x + 3))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

Popular Examples

(2x+3)(dy)/(dx)=y+(2x+3)^{1/2}

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

derivative of y=-4/(5x^5)+(15)/(4x^4)derivative of

y = - \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}}

derivative of f(x)=sqrt(x^2+21)derivative of

f (x) = x^{2} + 21

integral of 1/((x+3)^2(x-2))

\int \frac{1}{( x + 3 ) ^{2} ( x - 2 )} d x

derivative of x^22^x

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ln(x^3+5x+3) ?
The derivative of f(x)=ln(x^3+5x+3) is (3x^2+5)/(x^3+5x+3)
What is the first derivative of f(x)=ln(x^3+5x+3) ?
The first derivative of f(x)=ln(x^3+5x+3) is (3x^2+5)/(x^3+5x+3)