What is the derivative of f(x)=6sqrt(6x^{10)+7x^6} ?

The derivative of f(x)=6sqrt(6x^{10)+7x^6} is (3(60x^9+42x^5))/(sqrt(x^6)\sqrt{6x^4+7)}

What is the first derivative of f(x)=6sqrt(6x^{10)+7x^6} ?

The first derivative of f(x)=6sqrt(6x^{10)+7x^6} is (3(60x^9+42x^5))/(sqrt(x^6)\sqrt{6x^4+7)}

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derivative of

f (x) = 6 6 x^{10} + 7 x^{6}

\frac{3 ( 60 x ^{9} + 42 x ^{5} )}{x ^{6} 6 x ^{4} + 7}

Solution steps

\frac{d}{d x} (6 6 x^{10} + 7 x^{6})

Take the constant out:

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

= 6 \frac{d}{d x} (6 x^{10} + 7 x^{6})

Apply the chain rule:

\frac{1}{2 6 x ^{10} + 7 x ^{6}} \frac{d}{d x} (6 x^{10} + 7 x^{6})

= \frac{1}{2 6 x ^{10} + 7 x ^{6}} \frac{d}{d x} (6 x^{10} + 7 x^{6})

\frac{d}{d x} (6 x^{10} + 7 x^{6}) = 60 x^{9} + 42 x^{5}

= 6 \cdot \frac{1}{2 6 x ^{10} + 7 x ^{6}} (60 x^{9} + 42 x^{5})

Simplify

6 \cdot \frac{1}{2 6 x ^{10} + 7 x ^{6}} (60 x^{9} + 42 x^{5}) : \frac{3 ( 60 x ^{9} + 42 x ^{5} )}{x ^{6} 6 x ^{4} + 7}

= \frac{3 ( 60 x ^{9} + 42 x ^{5} )}{x ^{6} 6 x ^{4} + 7}

(0, - 10), (5, - 6)

\frac{d}{d x} (arcsinh (cot (x)))

\frac{\partial}{\partial x} (y cos (z))

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

x^{2} y^{^{''}} + 6 x y^{^{'}} + 6 y = 0

What is the derivative of f(x)=6sqrt(6x^{10)+7x^6} ?
The derivative of f(x)=6sqrt(6x^{10)+7x^6} is (3(60x^9+42x^5))/(sqrt(x^6)\sqrt{6x^4+7)}
What is the first derivative of f(x)=6sqrt(6x^{10)+7x^6} ?
The first derivative of f(x)=6sqrt(6x^{10)+7x^6} is (3(60x^9+42x^5))/(sqrt(x^6)\sqrt{6x^4+7)}