Calculus Examples

$\int_{- 19}^{x^{2}} {(t - 169)}^{92} {(5 t - 245)}^{37} d t$

Step 1

Take the derivative of $\int_{- 19}^{x^{2}} {(t - 169)}^{92} {(5 t - 245)}^{37} d t$ with respect to $x$ using Fundamental Theorem of Calculus and the chain rule.

$\frac{d}{d x} [x^{2}] ({(x^{2} - 169)}^{92} {(5 x^{2} - 245)}^{37})$

Step 2

Differentiate using the Power Rule.

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Step 2.1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2 x ({(x^{2} - 169)}^{92} {(5 x^{2} - 245)}^{37})$

Step 2.2

Reorder the factors of $2 x ({(x^{2} - 169)}^{92} {(5 x^{2} - 245)}^{37})$ .

$2 x {(x^{2} - 169)}^{92} {(5 x^{2} - 245)}^{37}$