What is the derivative of sqrt((x^27^x^9)) ?

The derivative of sqrt((x^27^x^9)) is (9*40353607^xx^8(ln(7)x+2))/(2sqrt(40353607^x))

What is the first derivative of sqrt((x^27^x^9)) ?

The first derivative of sqrt((x^27^x^9)) is (9*40353607^xx^8(ln(7)x+2))/(2sqrt(40353607^x))

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\frac{d}{d x} ((x^{2} 7^{x})^{9})

\frac{9 \cdot 4035360 7 ^{x} x ^{8} ( ln ( 7 ) x + 2 )}{2 4035360 7 ^{x}}

Solution steps

\frac{d}{d x} ((x^{2} \cdot 7^{x})^{9})

Apply the chain rule:

\frac{1}{2 ( x ^{2} \cdot 7 ^{x} ) ^{9}} \frac{d}{d x} ((x^{2} \cdot 7^{x})^{9})

= \frac{1}{2 ( x ^{2} \cdot 7 ^{x} ) ^{9}} \frac{d}{d x} ((x^{2} \cdot 7^{x})^{9})

\frac{d}{d x} ((x^{2} \cdot 7^{x})^{9}) = 9 ln (7) \cdot 4035360 7^{x} x^{18} + 18 x^{17} \cdot 4035360 7^{x}

= \frac{1}{2 ( x ^{2} \cdot 7 ^{x} ) ^{9}} (9 ln (7) \cdot 4035360 7^{x} x^{18} + 18 x^{17} \cdot 4035360 7^{x})

Simplify

\frac{1}{2 ( x ^{2} \cdot 7 ^{x} ) ^{9}} (9 ln (7) \cdot 4035360 7^{x} x^{18} + 18 x^{17} \cdot 4035360 7^{x}) : \frac{9 \cdot 4035360 7 ^{x} x ^{8} ( ln ( 7 ) x + 2 )}{2 4035360 7 ^{x}}

= \frac{9 \cdot 4035360 7 ^{x} x ^{8} ( ln ( 7 ) x + 2 )}{2 4035360 7 ^{x}}

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

\int sin (5 x) cos (5 x) d x

\int 2 \frac{1}{x} d x

\int e^{- 7 x} tan (e^{- 7 x}) d x

x y^{^{'}} + 2 y ln (x) = 3

What is the derivative of sqrt((x^27^x^9)) ?
The derivative of sqrt((x^27^x^9)) is (9*40353607^xx^8(ln(7)x+2))/(2sqrt(40353607^x))
What is the first derivative of sqrt((x^27^x^9)) ?
The first derivative of sqrt((x^27^x^9)) is (9*40353607^xx^8(ln(7)x+2))/(2sqrt(40353607^x))