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Popular >

derivative of f(x)=xsqrt(x^3-6)

Solution

derivative of

f (x) = x x^{3} - 6

Solution

\frac{5 x ^{3} - 12}{2 x ^{3} - 6}

Solution steps

\frac{d}{d x} (x x^{3} - 6)

Apply the Product Rule:

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

f = x, g = x^{3} - 6

= \frac{d x}{d x} x^{3} - 6 + \frac{d}{d x} (x^{3} - 6) x

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{3} - 6) = \frac{3 x ^{2}}{2 x ^{3} - 6}

= 1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x

Simplify

1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x : \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

= \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

Popular Examples

derivative of y=2x^2sqrt(2-x)derivative of

y = 2 x^{2} 2 - x

(\partial)/(\partial x)(e^{-1}cos(pix))

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

(dx}{dt}=\frac{2x)/t ,x(3)=1

\frac{d x}{d t} = \frac{2 x}{t}, x (3) = 1

tangent of f(x)=5e^x+3x,(0,5)tangent of

f (x) = 5 e^{x} + 3 x, (0, 5)

laplacetransform 10+t^2 laplace transform

10 + t^{2}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=xsqrt(x^3-6) ?
The derivative of f(x)=xsqrt(x^3-6) is (5x^3-12)/(2sqrt(x^3-6))
What is the first derivative of f(x)=xsqrt(x^3-6) ?
The first derivative of f(x)=xsqrt(x^3-6) is (5x^3-12)/(2sqrt(x^3-6))