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MrGoodyear812
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Help! I haven't the slightest clue on how to do this...
thanks in advance!
thanks in advance!
MrGoodyear812 said:Help! I haven't the slightest clue on how to do this...
thanks in advance!
The derivative of cos(x)^(x+7) is (-sin(x)^(x+7))*(ln(cos(x))*(x+7) + (x+7)*sin(x)/cos(x)).
To calculate the derivative of cos(x)^(x+7), you can use the power rule and the chain rule. First, rewrite cos(x)^(x+7) as e^(ln(cos(x)^(x+7))). Then, use the power rule to find the derivative of ln(cos(x)^(x+7)), and finally, apply the chain rule to the overall expression.
The derivative of cos(x)^(x+7) represents the rate of change of the function at any given point. It can be used to find the slope of the tangent line to the graph of the function and to determine the maximum and minimum values of the function.
Yes, the derivative of cos(x)^(x+7) can be simplified by using trigonometric identities and properties of logarithms. However, the simplified form may not always be more useful or meaningful than the original expression.
The derivatives of cos(x)^(x+7) and sin(x)^(x+7) are very similar, with the main difference being the negative sign in front of the sin(x) term in the derivative of cos(x)^(x+7). This is due to the negative derivative of cos(x) with respect to x compared to the positive derivative of sin(x) with respect to x.