What is the derivative of f(x)=sqrt(4x^2-5x) ?

The derivative of f(x)=sqrt(4x^2-5x) is (8x-5)/(2sqrt(4x^2-5x))

What is the first derivative of f(x)=sqrt(4x^2-5x) ?

The first derivative of f(x)=sqrt(4x^2-5x) is (8x-5)/(2sqrt(4x^2-5x))

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derivative of

f (x) = 4 x^{2} - 5 x

\frac{8 x - 5}{2 4 x ^{2} - 5 x}

Solution steps

\frac{d}{d x} (4 x^{2} - 5 x)

Apply the chain rule:

\frac{1}{2 4 x ^{2} - 5 x} \frac{d}{d x} (4 x^{2} - 5 x)

= \frac{1}{2 4 x ^{2} - 5 x} \frac{d}{d x} (4 x^{2} - 5 x)

\frac{d}{d x} (4 x^{2} - 5 x) = 8 x - 5

= \frac{1}{2 4 x ^{2} - 5 x} (8 x - 5)

Simplify

\frac{1}{2 4 x ^{2} - 5 x} (8 x - 5) : \frac{8 x - 5}{2 4 x ^{2} - 5 x}

= \frac{8 x - 5}{2 4 x ^{2} - 5 x}

What is the derivative of f(x)=sqrt(4x^2-5x) ?
The derivative of f(x)=sqrt(4x^2-5x) is (8x-5)/(2sqrt(4x^2-5x))
What is the first derivative of f(x)=sqrt(4x^2-5x) ?
The first derivative of f(x)=sqrt(4x^2-5x) is (8x-5)/(2sqrt(4x^2-5x))