What is (\partial)/(\partial x)(ysqrt(1+x^7)) ?

The answer to (\partial)/(\partial x)(ysqrt(1+x^7)) is (7yx^6)/(2sqrt(1+x^7))

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(\partial)/(\partial x)(ysqrt(1+x^7))

\frac{\partial}{\partial x} (y 1 + x^{7})

\frac{7 y x ^{6}}{2 1 + x ^{7}}

Solution steps

\frac{\partial}{\partial x} (y 1 + x^{7})

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (1 + x^{7})

Apply the chain rule:

\frac{1}{2 1 + x ^{7}} \frac{\partial}{\partial x} (1 + x^{7})

= \frac{1}{2 1 + x ^{7}} \frac{\partial}{\partial x} (1 + x^{7})

\frac{\partial}{\partial x} (1 + x^{7}) = 7 x^{6}

= y \frac{1}{2 1 + x ^{7}} \cdot 7 x^{6}

Simplify

y \frac{1}{2 1 + x ^{7}} \cdot 7 x^{6} : \frac{7 y x ^{6}}{2 1 + x ^{7}}

= \frac{7 y x ^{6}}{2 1 + x ^{7}}

\int \frac{11 x ^{2}}{( 144 + x ^{2} ) ^{2}} d x

\frac{d}{d x} (x^{6} ln (7 x))

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

\frac{d}{d x} (x^{\frac{9}{4}})

f (θ) = 11 θ

What is (\partial)/(\partial x)(ysqrt(1+x^7)) ?
The answer to (\partial)/(\partial x)(ysqrt(1+x^7)) is (7yx^6)/(2sqrt(1+x^7))