What is the derivative of-3/(16(1+x^{7/4)}) ?

The derivative of-3/(16(1+x^{7/4)}) is (21)/(64(1+x)^{11/4)}

What is the first derivative of-3/(16(1+x^{7/4)}) ?

The first derivative of-3/(16(1+x^{7/4)}) is (21)/(64(1+x)^{11/4)}

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\frac{d}{d x} (- \frac{3}{16 ( 1 + x ) ^{\frac{7}{4}}})

\frac{21}{64 ( 1 + x ) ^{\frac{11}{4}}}

Solution steps

\frac{d}{d x} (- \frac{3}{16 ( 1 + x ) ^{\frac{7}{4}}})

Take the constant out:

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

= - \frac{3}{16} \frac{d}{d x} (\frac{1}{( 1 + x ) ^{\frac{7}{4}}})

Apply exponent rule:

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

= - \frac{3}{16} \frac{d}{d x} ((1 + x)^{- \frac{7}{4}})

Apply the chain rule:

- \frac{7}{4 ( 1 + x ) ^{\frac{11}{4}}} \frac{d}{d x} (1 + x)

= - \frac{7}{4 ( 1 + x ) ^{\frac{11}{4}}} \frac{d}{d x} (1 + x)

\frac{d}{d x} (1 + x) = 1

= - \frac{3}{16} (- \frac{7}{4 ( 1 + x ) ^{\frac{11}{4}}} \cdot 1)

Simplify

- \frac{3}{16} (- \frac{7}{4 ( 1 + x ) ^{\frac{11}{4}}} \cdot 1) : \frac{21}{64 ( 1 + x ) ^{\frac{11}{4}}}

= \frac{21}{64 ( 1 + x ) ^{\frac{11}{4}}}

\int 4 e^{x} 4 + e^{x} d x

\frac{d}{d x} ((2 x + 1)^{6})

\int_{- 1}^{2} (x^{2} - 3 x) d x

\frac{d x}{d y} = \frac{x ^{2} y + y ^{3}}{x}

\frac{\partial}{\partial x} (cos^{3} (x^{8} y^{8}))

What is the derivative of-3/(16(1+x^{7/4)}) ?
The derivative of-3/(16(1+x^{7/4)}) is (21)/(64(1+x)^{11/4)}
What is the first derivative of-3/(16(1+x^{7/4)}) ?
The first derivative of-3/(16(1+x^{7/4)}) is (21)/(64(1+x)^{11/4)}