What is the derivative of arcsin(x^7) ?

The derivative of arcsin(x^7) is (7x^6)/(sqrt(1-x^{14))}

What is the first derivative of arcsin(x^7) ?

The first derivative of arcsin(x^7) is (7x^6)/(sqrt(1-x^{14))}

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derivative of

arcsin (x^{7})

\frac{7 x ^{6}}{1 - x ^{14}}

Solution steps

\frac{d}{d x} (arcsin (x^{7}))

Apply the chain rule:

\frac{1}{1 - ( x ^{7} ) ^{2}} \frac{d}{d x} (x^{7})

= \frac{1}{1 - ( x ^{7} ) ^{2}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{1}{1 - ( x ^{7} ) ^{2}} \cdot 7 x^{6}

Simplify

\frac{1}{1 - ( x ^{7} ) ^{2}} \cdot 7 x^{6} : \frac{7 x ^{6}}{1 - x ^{14}}

= \frac{7 x ^{6}}{1 - x ^{14}}

\frac{d}{d x} (e^{3 x} - \frac{6}{x})

2 x \cdot e^{2 x}

\int \frac{t}{1 - t ^{2}} d t

\frac{d}{d x} (2 x^{2} - 4 x + 4)

- 8 x^{2} + 500 x + 140

What is the derivative of arcsin(x^7) ?
The derivative of arcsin(x^7) is (7x^6)/(sqrt(1-x^{14))}
What is the first derivative of arcsin(x^7) ?
The first derivative of arcsin(x^7) is (7x^6)/(sqrt(1-x^{14))}