What is (\partial)/(\partial x)(log_{3}(7^{x^2-4})) ?

The answer to (\partial)/(\partial x)(log_{3}(7^{x^2-4})) is 2log_{3}(7)x

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(\partial)/(\partial x)(log_{3}(7^{x^2-4}))

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

2 lo g_{3} (7) x

Solution steps

\frac{\partial}{\partial x} (lo g_{3} (7^{x^{2} - 4}))

Simplify

lo g_{3} (7^{x^{2} - 4}) : lo g_{3} (7) (x^{2} - 4)

= \frac{\partial}{\partial x} (lo g_{3} (7) (x^{2} - 4))

Take the constant out:

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

= lo g_{3} (7) \frac{\partial}{\partial x} (x^{2} - 4)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= lo g_{3} (7) (\frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (4) = 0

= lo g_{3} (7) (2 x - 0)

Simplify

= 2 lo g_{3} (7) x

\int_{0}^{5} (5 x^{2} - x^{3}) d x

\int \frac{5}{4 - 3 x} d x

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

\frac{\partial}{\partial x} (sin (5 x y + 4 yz + 7 x z))

f (x) = \frac{- 8 x}{x ^{2} + 1}, (0, 0)

What is (\partial)/(\partial x)(log_{3}(7^{x^2-4})) ?
The answer to (\partial)/(\partial x)(log_{3}(7^{x^2-4})) is 2log_{3}(7)x