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  • Let  be a function defined by<img alt="f(x)=e^{x2}-x^{3}" src="https://entrancecorne

Let f(x) be a function defined byf(x)=e^{x2}-x^{3} . The derivative of f(x) with respect to x, denoted  as f{}'(x), is given by f{}'(x) = ________.

 

Option: 1

f^{\prime}(x)=2 x * e^{\left(x^2\right)}-3 x^2


Option: 2

f^{\prime}(x)=2 x * e^{\left(x^2\right)}-6 x


Option: 3

f^{\prime}(x)=2 x * e^{\left(x^2\right)}+6 x


Option: 4

f^{\prime}(x)=2 x * e^{\left(x^2\right)}+3 x^2


Answers (1)

best_answer

To find the derivative of f(x), to differentiate each term of the function separately using the appropriate rules of differentiation.

Given  f(x)=e^{\left(x^2\right)}-x^3

Differentiating the first terme(x^{2}), , with respect to x, we apply the chain rule:

\frac{d e^{\left(x^2\right)}}{d x}=e^{\left(x^2\right)} *(2 x)=2 x * e^{\left(x^2\right)}

Differentiating the second term,-x^{3} with respect to x, use the power rule:

\frac{d\left(-x^3\right)}{d x}=-3 x^2

Now,  combine the derivatives of the individual terms to find the derivative of f(x)

f^{\prime}(x)=2 x * e^{\left(x^2\right)}-3 x^2

Therefore, the derivative of  f(x) with respect to x f{}'(x), is given by:

f^{\prime}(x)=2 x * e^{\left(x^2\right)}-3 x^2


 

 

 

 

Posted by

HARSH KANKARIA

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