What is the derivative of sqrt((x^2*5^x^9)) ?

The derivative of sqrt((x^2*5^x^9)) is (9*1953125^xx^8(ln(5)x+2))/(2sqrt(1953125^x))

What is the first derivative of sqrt((x^2*5^x^9)) ?

The first derivative of sqrt((x^2*5^x^9)) is (9*1953125^xx^8(ln(5)x+2))/(2sqrt(1953125^x))

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\frac{d}{d x} ((x^{2} \cdot 5^{x})^{9})

\frac{9 \cdot 195312 5 ^{x} x ^{8} ( ln ( 5 ) x + 2 )}{2 195312 5 ^{x}}

Solution steps

\frac{d}{d x} ((x^{2} \cdot 5^{x})^{9})

Apply the chain rule:

\frac{1}{2 ( x ^{2} \cdot 5 ^{x} ) ^{9}} \frac{d}{d x} ((x^{2} \cdot 5^{x})^{9})

= \frac{1}{2 ( x ^{2} \cdot 5 ^{x} ) ^{9}} \frac{d}{d x} ((x^{2} \cdot 5^{x})^{9})

\frac{d}{d x} ((x^{2} \cdot 5^{x})^{9}) = 9 ln (5) \cdot 195312 5^{x} x^{18} + 18 x^{17} \cdot 195312 5^{x}

= \frac{1}{2 ( x ^{2} \cdot 5 ^{x} ) ^{9}} (9 ln (5) \cdot 195312 5^{x} x^{18} + 18 x^{17} \cdot 195312 5^{x})

Simplify

\frac{1}{2 ( x ^{2} \cdot 5 ^{x} ) ^{9}} (9 ln (5) \cdot 195312 5^{x} x^{18} + 18 x^{17} \cdot 195312 5^{x}) : \frac{9 \cdot 195312 5 ^{x} x ^{8} ( ln ( 5 ) x + 2 )}{2 195312 5 ^{x}}

= \frac{9 \cdot 195312 5 ^{x} x ^{8} ( ln ( 5 ) x + 2 )}{2 195312 5 ^{x}}

x \to 0 lim (\frac{7}{x} - \frac{7}{x ^{2} - x})

x y^{^{''}} + 2 y^{^{'}} - 4 = 0

x y^{^{'}} + y = 3 x y^{2}

\frac{\partial}{\partial y} (x^{2} y + 3 x y^{4})

\frac{d}{d x} (7 x^{\frac{3}{2}})

What is the derivative of sqrt((x^2*5^x^9)) ?
The derivative of sqrt((x^2*5^x^9)) is (9*1953125^xx^8(ln(5)x+2))/(2sqrt(1953125^x))
What is the first derivative of sqrt((x^2*5^x^9)) ?
The first derivative of sqrt((x^2*5^x^9)) is (9*1953125^xx^8(ln(5)x+2))/(2sqrt(1953125^x))