What is the derivative of (600/(1+49(0.6)^x)) ?

The derivative of (600/(1+49(0.6)^x)) is (15018.27333…*0.6^x)/((1+49*0.6^x)^2)

What is the first derivative of (600/(1+49(0.6)^x)) ?

The first derivative of (600/(1+49(0.6)^x)) is (15018.27333…*0.6^x)/((1+49*0.6^x)^2)

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\frac{d}{d x} (\frac{600}{1 + 49 ( 0.6 ) ^{x}})

\frac{15018.27333 \dots \cdot 0. 6 ^{x}}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{600}{1 + 49 ( 0.6 ) ^{x}})

Take the constant out:

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

= 600 \frac{d}{d x} (\frac{1}{1 + 49 \cdot 0. 6 ^{x}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 600 \frac{d}{d x} ((1 + 49 \cdot 0. 6^{x})^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}} \frac{d}{d x} (1 + 49 \cdot 0. 6^{x})

= - \frac{1}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}} \frac{d}{d x} (1 + 49 \cdot 0. 6^{x})

\frac{d}{d x} (1 + 49 \cdot 0. 6^{x}) = - 25.03045 \dots \cdot 0. 6^{x}

= 600 (- \frac{1}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}} (- 25.03045 \dots \cdot 0. 6^{x}))

Simplify

600 (- \frac{1}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}} (- 25.03045 \dots \cdot 0. 6^{x})) : \frac{15018.27333 \dots \cdot 0. 6 ^{x}}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}}

= \frac{15018.27333 \dots \cdot 0. 6 ^{x}}{( 1 + 49 \cdot 0. 6 ^{x} ) ^{2}}

\frac{d}{d x} (2 x + y^{2} - z^{2})

\frac{d}{d x} (10 tan (x))

\frac{d}{d X} (X Y + Y Z (Y + Z))

n = 0 \sum \infty \frac{n !}{3 n ! - 1}

e^{x} x - 6 e^{x}

What is the derivative of (600/(1+49(0.6)^x)) ?
The derivative of (600/(1+49(0.6)^x)) is (15018.27333…*0.6^x)/((1+49*0.6^x)^2)
What is the first derivative of (600/(1+49(0.6)^x)) ?
The first derivative of (600/(1+49(0.6)^x)) is (15018.27333…*0.6^x)/((1+49*0.6^x)^2)