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Popular >

derivative of y=x(5^{-3x})

Solution

derivative of

y = x (5^{- 3 x})

Solution

- 3 ln (5) \cdot 12 5^{- x} x + 12 5^{- x}

Solution steps

\frac{d}{d x} (x \cdot 5^{- 3 x})

Simplify

x \cdot 5^{- 3 x} : 12 5^{- x} x

= \frac{d}{d x} (12 5^{- x} x)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 12 5^{- x}, g = x

= \frac{d}{d x} (12 5^{- x}) x + \frac{d x}{d x} 12 5^{- x}

\frac{d}{d x} (12 5^{- x}) = - 3 ln (5) \cdot 12 5^{- x}

\frac{d x}{d x} = 1

= (- 3 ln (5) \cdot 12 5^{- x}) x + 1 \cdot 12 5^{- x}

Simplify

= - 3 ln (5) \cdot 12 5^{- x} x + 12 5^{- x}

Popular Examples

derivative of (3e^x/(5e^x+4))

\frac{d}{d x} (\frac{3 e ^{x}}{5 e ^{x} + 4})

derivative of sin^{n-1}(x)

\frac{d}{d x} (sin^{n - 1} (x))

tangent of f(x)=-3/(x^2-4),(1,1)tangent of

f (x) = - \frac{3}{x ^{2} - 4}, (1, 1)

limit as x approaches 0 of x^6sin(6/x)

x \to 0 lim (x^{6} sin (\frac{6}{x}))

(dy)/(dt)=cos(t)

\frac{d y}{d t} = cos (t)

Frequently Asked Questions (FAQ)

What is the derivative of y=x(5^{-3x}) ?
The derivative of y=x(5^{-3x}) is -3ln(5)*125^{-x}x+125^{-x}
What is the first derivative of y=x(5^{-3x}) ?
The first derivative of y=x(5^{-3x}) is -3ln(5)*125^{-x}x+125^{-x}