What is the derivative of (x-7/((x+5)^{10)}) ?

The derivative of (x-7/((x+5)^{10)}) is (3(-3x+25))/((x+5)^{11)}

What is the first derivative of (x-7/((x+5)^{10)}) ?

The first derivative of (x-7/((x+5)^{10)}) is (3(-3x+25))/((x+5)^{11)}

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\frac{d}{d x} (\frac{x - 7}{( x + 5 ) ^{10}})

\frac{3 ( - 3 x + 25 )}{( x + 5 ) ^{11}}

Solution steps

\frac{d}{d x} (\frac{x - 7}{( x + 5 ) ^{10}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x - 7 ) ( x + 5 ) ^{10} - \frac{d}{d x} ( ( x + 5 ) ^{10} ) ( x - 7 )}{( ( x + 5 ) ^{10} ) ^{2}}

\frac{d}{d x} (x - 7) = 1

\frac{d}{d x} ((x + 5)^{10}) = 10 (x + 5)^{9}

= \frac{1 \cdot ( x + 5 ) ^{10} - 10 ( x + 5 ) ^{9} ( x - 7 )}{( ( x + 5 ) ^{10} ) ^{2}}

Simplify

\frac{1 \cdot ( x + 5 ) ^{10} - 10 ( x + 5 ) ^{9} ( x - 7 )}{( ( x + 5 ) ^{10} ) ^{2}} : \frac{3 ( - 3 x + 25 )}{( x + 5 ) ^{11}}

= \frac{3 ( - 3 x + 25 )}{( x + 5 ) ^{11}}

x^{2} - 12 x + k

x \to 4 lim (x 25 - x^{2})

y^{^{''}} + 4 y^{^{'}} + 12 y = 0

\int_{0}^{4} (13 - t) t d t

y = t^{2} + 5 cos (t)

What is the derivative of (x-7/((x+5)^{10)}) ?
The derivative of (x-7/((x+5)^{10)}) is (3(-3x+25))/((x+5)^{11)}
What is the first derivative of (x-7/((x+5)^{10)}) ?
The first derivative of (x-7/((x+5)^{10)}) is (3(-3x+25))/((x+5)^{11)}